CN116384204B - Finite element simulation method, system and related equipment for mixed unit order - Google Patents
Finite element simulation method, system and related equipment for mixed unit order Download PDFInfo
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Abstract
The invention is suitable for the technical field of wireless communication, and particularly relates to a finite element simulation method, a finite element simulation system and related equipment for mixed unit orders. The invention provides a method for modeling a grid type by adopting high-order and low-order unit collocation in filter device simulation based on a finite element method, which is characterized in that units with different orders are assembled in a model, and conflict nodes in the high-order units are restrained and the degree of freedom of the conflict nodes is eliminated by utilizing interpolation characteristics of the low-order units, so that the overall degree of freedom of a filter device model constructed in simulation is reduced on the premise of ensuring the calculation precision, the calculation dimension is reduced, and the overall calculation efficiency of a simulation process is improved.
Description
Technical Field
The invention is suitable for the technical field of wireless communication, and particularly relates to a finite element simulation method, a finite element simulation system and related equipment for mixed unit orders.
Background
Along with the development of wireless communication technology, the requirements of electronic consumer products on radio frequency devices are increasing, correspondingly, in the design process of the radio frequency devices, the requirements of designers on the frequency sweeping efficiency and accuracy of simulation software are also increasing, and the finite element method is an effective simulation algorithm.
Simulation based on the finite element method generally uses a finite number of simple grid cells to represent complex objects by discretizing the structure, the grid cells are connected with each other through a finite number of nodes and modeled, and then comprehensive numerical solution is carried out through modes such as solid mechanics, electrostatic control equations, boundary conditions and the like. Therefore, the finite element method can realize nearly uniform simulation precision for any complex geometric body and has higher convergence. However, when the number of divided grid cells is large, the calculation efficiency is greatly reduced.
For grid cells pre-divided by using a finite element method, the prior art can solve the problem of calculation efficiency by using acceleration methods such as GPU calculation, hierarchical cascading technology and the like. Because the simulation precision and the grid division have higher relevance, the self-adaptive grid technology is also proposed, and the self-adaptive grid technology performs grid refinement in a region with higher calculation precision requirement according to no-difference evaluation in the calculation process, and adopts coarser grid division with lower calculation precision requirement, so that the simulation efficiency is fully improved on the premise of ensuring the calculation precision.
However, although the adaptive grid technology can better balance the grid precision and the calculation speed, the adaptive grid technology depends on the evaluation of simulation errors, and grid refinement and coarsening behaviors in the simulation process are required to be obtained through multiple iterations, so that the adaptive grid technology is more suitable for the simulation problem that model parameters such as steady-state analysis are not changed. The simulation of the radio frequency device, especially the simulation of the elastic wave device, usually carries out sweep frequency calculation on different frequency points in a frequency band range, so if each frequency point adopts an adaptive grid technology to adjust the grid, the simulation efficiency is reduced due to the calculation problem of the grid.
For the common pre-partitioned grid technology, in order to ensure the simulation precision, a finer grid is often drawn and a higher unit order, such as a second-order Lagrangian quadrilateral grid, is adopted. However, in the simulation of the elastic wave device, the distribution of the physical field tends to have strong regularity, for example, when the surface acoustic wave device is simulated, the elastic energy of the surface acoustic wave device tends to be concentrated in a range of one wavelength on the surface of the device. In the simulation process of the prior art, a technician can use denser grids for a substrate and an electrode in a wavelength range of the surface acoustic wave device surface as shown in fig. 1 according to experience, and sparse grids are used outside the wavelength, and the dense grids and the sparse grids can also use grids with proper lengths for transition. However, since the whole surface acoustic wave device adopts a higher unit order, the degree of freedom of the whole surface acoustic wave device model constructed by the surface acoustic wave device model is still higher even if a sparse grid is adopted at a position far away from the surface, so that the calculation dimension is larger, and the simulation efficiency is still lower.
Disclosure of Invention
The invention provides a finite element simulation method, a finite element simulation system and related equipment for mixed unit orders, and aims to solve the problems that in the prior art, in the simulation process of a filter device based on the finite element method, a simulation model obtained by using a pre-divided grid is high in degree of freedom and large in calculation dimension.
In a first aspect, the present invention provides a finite element simulation method of mixed unit order, the finite element simulation method is used for simulating a filter device based on a finite element method, and the finite element simulation method includes the following steps:
s1, acquiring the geometric structure of the filter device;
s2, splitting the filter device into a plurality of interdigital structures according to the positions of electrode metals according to the geometric structures, wherein the interdigital structures are divided into a first wavelength region and a second wavelength region according to the wavelength performance of elastic waves;
s3, dividing the first wavelength region into a plurality of first grids, and dividing the second wavelength region into a plurality of second grids;
s4, modeling each first grid by adopting a preset high-order unit based on a finite element method to obtain a corresponding high-order matrix; simultaneously, modeling each second grid by adopting a preset low-order unit to obtain a corresponding low-order matrix; wherein, the preset high-order unit and the preset low-order unit have different unit orders;
s5, splicing the high-order matrix and the low-order matrix according to the positions of the first wavelength region and the second wavelength region to obtain a combined matrix of the interdigital structure, wherein the splicing positions of the high-order matrix and the low-order matrix are provided with conflict nodes with non-coincident transverse coordinates;
s6, restraining the conflict nodes in the combination matrix by adopting a preset numerical constraint method to obtain a second combination matrix;
and S7, splicing the second combination matrixes of different interdigital structures according to the geometric structures to obtain an overall matrix of the filter device, calculating a frequency response curve of the filter device based on the overall matrix, and outputting the frequency response curve as a simulation result.
Still further, step S5 comprises the sub-steps of:
acquiring the higher-order unit orders of the preset higher-order units and the lower-order unit orders of the preset lower-order units, and calculating the number of conflict nodes according to the higher-order unit orders and the lower-order unit orders;
acquiring the transverse coordinates of each conflict node, and constructing an interpolation expression for calculating the degree of freedom of the node in the preset low-order unit according to the low-order unit orders;
substituting the coordinates of each conflict node into the interpolation polynomials respectively for calculation to obtain the degree of freedom of the conflict node;
and combining the degrees of freedom of all the conflict nodes into the preset low-order unit for calculation to obtain the combination matrix.
Still further, the interpolation expression satisfies the following relational expression (1):
（1）；
and:
（2）；
in the relational expressions (1) and (2),nthe number of orders of the cells is indicated,kis a node in the preset low-order unit, and1≤k≤n+ 1，xrepresenting the lateral coordinates of the nodes in the preset low-order cell,ythe degree of freedom of the node in the preset low-order unit is valued,P n+1 (x)representing the unit order asnThe transverse coordinates in the preset low-order unit are as followsxIs a node of the first class.
Further, the preset numerical constraint method is a penalty function method.
Further, the degrees of freedom of the conflicting nodes are defined asa 2 The degrees of freedom of the left adjacent node and the right adjacent node of the conflict node in the transverse direction are respectivelya 1 、a 3 The degrees of freedom of the conflicting nodes satisfy the interpolation constraint of the following relation (3):
（3）。
further, the first grid has a different concentration in the first wavelength region than the second grid has in the second wavelength region.
In a second aspect, the present invention also provides a finite element simulation system of mixed unit order, the finite element simulation system being used for simulation of a filter device based on a finite element method, the finite element simulation system comprising:
the geometric acquisition module is used for acquiring the geometric structure of the filter device;
the geometrical difference module is used for dividing the filter device into a plurality of interdigital structures according to the geometrical structure and the positions of electrode metals, and the interdigital structures are divided into a first wavelength region and a second wavelength region according to the wavelength performance of elastic waves;
the grid dividing module is used for dividing the first wavelength region into a plurality of first grids and dividing the second wavelength region into a plurality of second grids;
the finite element modeling module is used for modeling each first grid by adopting a preset high-order unit based on a finite element method to obtain a corresponding high-order matrix; simultaneously, modeling each second grid by adopting a preset low-order unit to obtain a corresponding low-order matrix; wherein, the preset high-order unit and the preset low-order unit have different unit orders;
the finite element splicing module is used for splicing the high-order matrix and the low-order matrix according to the positions of the first wavelength region and the second wavelength region to obtain a combined matrix of the interdigital structure, wherein the splicing position of the high-order matrix and the low-order matrix is provided with a conflict node with non-coincident transverse coordinates;
the constraint module is used for constraining the conflict nodes in the combination matrix by adopting a preset numerical constraint method to obtain a second combination matrix;
and the output module is used for splicing the second combination matrixes of different interdigital structures according to the geometric structures to obtain an overall matrix of the filter device, calculating a frequency response curve of the filter device based on the overall matrix, and outputting the frequency response curve as a simulation result.
Still further, the finite element splicing module is specifically configured to:
acquiring the higher-order unit orders of the preset higher-order units and the lower-order unit orders of the preset lower-order units, and calculating the number of conflict nodes according to the higher-order unit orders and the lower-order unit orders;
acquiring the transverse coordinates of each conflict node, and constructing an interpolation expression for calculating the degree of freedom of the node in the preset low-order unit according to the low-order unit orders;
substituting the coordinates of each conflict node into the interpolation polynomials respectively for calculation to obtain the degree of freedom of the conflict node;
and combining the degrees of freedom of all the conflict nodes into the preset low-order unit for calculation to obtain the combination matrix.
In a third aspect, the present invention also provides a computer device comprising: a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps in the mixed unit order finite element simulation method according to any of the above embodiments when the computer program is executed.
In a fourth aspect, the present invention also provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the finite element simulation method of mixed cell orders as described in any of the above embodiments.
The invention has the beneficial effects that the invention provides a method for modeling the grid type by adopting the matching of high-order units and low-order units in the filter device simulation based on the finite element method, units with different orders are assembled in the model, and the conflict nodes in the high-order units are restrained and the degree of freedom of the conflict nodes is eliminated by utilizing the interpolation characteristic of the low-order units, so that the overall degree of freedom of the filter device model constructed by simulation is reduced on the premise of ensuring the calculation precision, the calculation dimension is reduced, and the overall calculation efficiency of the simulation process is improved.
Drawings
FIG. 1 is a meshing schematic diagram of a prior art adaptive meshing technique;
FIG. 2 is a block flow diagram of steps of a finite element simulation method for mixed unit orders provided by an embodiment of the present invention;
FIG. 3 is a schematic diagram of simulation modeling of a mixed-order cell provided by an embodiment of the present invention;
FIG. 4 is a schematic diagram of a second order Lagrangian cell matrix mutual stitching provided by an embodiment of the present invention;
FIG. 5 is a schematic diagram of a Lagrangian cell matrix splice with different cell orders according to an embodiment of the present invention;
FIG. 6 is a schematic view of degrees of freedom of Lagrangian cell matrix stitching for different cell orders provided by an embodiment of the present invention;
FIG. 7 is a schematic diagram of a finite element simulation system with mixed unit orders according to an embodiment of the present invention;
fig. 8 is a schematic structural diagram of a computer device according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Referring to fig. 2, fig. 2 is a block flow diagram of steps of a finite element simulation method of mixed unit order, which is used for simulating a filter device based on the finite element method, and the finite element simulation method includes the following steps:
s1, acquiring the geometric structure of the filter device.
The embodiment of the invention is described by taking the elastic wave device in the filter device as an example, and it should be noted that the method of the embodiment of the invention can be utilized in any device simulation with the characteristics of the filter device, and is not limited to the elastic wave device, and the geometric structure can be a process design diagram of the elastic wave device or a structure diagram obtained by actual measurement.
S2, splitting the filter device into a plurality of interdigital structures according to the positions of electrode metals according to the geometric structures, wherein the interdigital structures are divided into a first wavelength region and a second wavelength region according to the wavelength performance of elastic waves.
In the embodiment of the invention, the finger-inserting structure comprises electrode metal and a substrate part connected with the electrode metal, the wavelength performance of elastic waves shown by the finger-inserting structure is usually concentrated in a range of only one wavelength on the surface of the device, generally, the first wavelength region is close to the position of the electrode metal, and the second wavelength region is far from the electrode metal. It is conceivable that, according to the actual structure and the simulation requirement of the elastic wave device to be simulated, two or more wavelength regions may be divided according to the size of the elastic wave, and in the subsequent step, different types of grids may be used for simulation modeling for different wavelength regions, but the principle when the grids are spliced is still the same as that in the embodiment of the present invention.
S3, dividing the first wavelength region into a plurality of first grids, and dividing the second wavelength region into a plurality of second grids.
Compared with the self-adaptive grid technology in the prior art, the grid division mode in the embodiment of the invention needs to be set according to quadrilateral units with different unit orders used in the subsequent steps. Further, the first grid has a different concentration in the first wavelength region than the second grid has in the second wavelength region.
S4, modeling each first grid by adopting a preset high-order unit based on a finite element method to obtain a corresponding high-order matrix; simultaneously, modeling each second grid by adopting a preset low-order unit to obtain a corresponding low-order matrix; the preset high-order unit and the preset low-order unit have different unit orders.
Referring to fig. 3, fig. 3 is a schematic diagram of simulation modeling of a mixed-order unit according to an embodiment of the present invention, in which a second-order lagrangian quadrangle unit is used as the preset high-order unit, a first-order lagrangian quadrangle unit is used as the preset low-order matrix to perform unit assembly, and the difference between different-order lagrangian quadrangle units is that the number of nodes in the grid is different, i.e. the unit orders are different, for example, the first-order lagrangian quadrangle unit has four nodes, and the second-order lagrangian quadrangle unit has nine nodes.
And S5, splicing the high-order matrix and the low-order matrix according to the positions of the first wavelength region and the second wavelength region to obtain a combined matrix of the interdigital structure, wherein the splicing positions of the high-order matrix and the low-order matrix are provided with conflict nodes with non-coincident transverse coordinates.
In the elastic wave device simulation in the prior art, since the unit types with the same unit order are generally adopted, different grids can be assembled easily, as shown in fig. 4, when the unit matrixes of the same second-order Lagrange units are mutually spliced, the units on the spliced edges are respectively provided with three nodes, and the freedom degree continuity of the assembled boundary is ensured, so that the two grids can be directly combined at the nodes, the middle three nodes are shared, in the elastic wave device simulation, the nodes have the physical attribute of the physical field freedom degree, so that the simulation calculation of parameters is realized, and the values of the freedom degrees solved by the three shared nodes are completely the same in the two units on the premise that the unit orders are the same.
In the embodiment of the present invention, since the units with different unit orders are spliced, for example, the first-order lagrangian quadrilateral unit and the second-order lagrangian quadrilateral unit, there may be a situation that the units shown in fig. 5 cannot be completely assembled, in this case, two corner nodes at two grid corners are shared, and edge nodes in the second-order lagrangian quadrilateral unit are not shared, so that only the values of degrees of freedom solved by two shared nodes are completely the same in the two units, but the units at the edge nodes which are not shared are collision nodes, and the degrees of freedom values of the collision nodes are different in the results calculated in the two units.
Therefore, in order to solve the problem that the result of calculation of the value of the degree of freedom at the conflict node in two cells is different, in the mesh division method using cells of different cell orders.
In order to solve the above problem, step S5 further includes the following sub-steps:
s51, obtaining the higher-order unit orders of the preset higher-order units and the lower-order unit orders of the preset lower-order units, and calculating the number of conflict nodes according to the higher-order unit orders and the lower-order unit orders.
S52, acquiring the transverse coordinates of each conflict node, and constructing an interpolation expression for calculating the degree of freedom of the node in the preset low-order unit according to the low-order unit order.
In the embodiment of the invention, the third-order Lagrangian quadrilateral unit is taken as the preset high-order unit, and the second-order Lagrangian quadrilateral unit is taken as the preset low-order matrix for the calculation and the explanation of the interpolation expression, because the assembly of different unit orders only relates to the simulation of the interdigital structurexConflict nodes of the direction are spliced toyNo splicing is required, so the embodiment of the invention definesxIs a transverse coordinate in a horizontal coordinate system,yto take the value of the degree of freedom to be calculated, as shown in FIG. 6, the lateral coordinates arex1、x3Will be the common node, and sit horizontallyMarked asx2、x4、x5I.e. the collision node for which interpolation is to be performed.
Still further, the interpolation expression satisfies the following relational expression (1):
（1）；
and:
（2）；
in the relational expressions (1) and (2),nthe number of orders of the cells is indicated,kis a node in the preset low-order unit, and1≤k≤n+ 1，xrepresenting the lateral coordinates of the nodes in the preset low-order cell,ythe degree of freedom of the node in the preset low-order unit is valued,P n+1 (x)representing the unit order asnThe transverse coordinates in the preset low-order unit are as followsxIs a node of the first class.
For example, for the concatenation of the Lagrangian quadrilateral elements of the second and third order in FIG. 6, the degree of freedom is taken in the Lagrangian quadrilateral elements of the second ordery(x)Along with coordinatesxThe following expression is satisfied by the variation of (a):
；
for a second order Lagrangian quadrilateral, the lateral coordinates of the collision nodes are x4, x5.
And S53, substituting the coordinates of each conflict node into the interpolation polynomials for calculation to obtain the degree of freedom of the conflict node.
Further, for the transverse coordinates, respectivelyx4、x5Of their respective degrees of freedomy4、y5The following relationship is satisfied:
；
。
s54, combining the degrees of freedom of all the conflict nodes into the preset low-order unit for calculation to obtain the combination matrix.
In the concatenation of Lagrangian quadrilateral elements of second and third order, according to the specificsx1、x2、x3、x4、x5Is substituted into the expression in the step S53 to be simplified, and the obtained value is obtainedy4And (3) withy1、y2、y3And (2) a relation ofy5And (3) withy1、y2、y3The degrees of freedom of the collision nodes and the mutual overlapping nodes in the splicing process can be expressed respectively, namely the splicing of Lagrange quadrilateral units with mixed unit orders is completed, and the matrix obtained based on the splicing can be expressed as the combined matrix between the first grid and the second grid according to a finite element method.
S6, restraining the conflict nodes in the combination matrix by adopting a preset numerical value restraining method to obtain a second combination matrix.
Because the grid division method of the units with different unit orders also needs to solve the problem that the calculated results of the degrees of freedom values at the conflict nodes in the two units are different, the embodiment of the invention also needs to restrict the degrees of freedom of the edge nodes in the higher-order Lagrangian quadrilateral units so that the edge nodes meet the linear interpolation rule consistent with the lower-order Lagrangian units.
The finite element method is calculated by multiplying the combination matrix by the degree of freedom matrixThereby calculating and obtaining the value of the degree of freedom of each node +.>Therefore, embodiments of the present invention also differ from prior art finite element method simulations in that the setComposite matrix->And performing constraint processing, wherein the preset numerical constraint method is a penalty function method. For example, for a product of a combination matrix and a degree of freedom matrix:
；
defining the degrees of freedom of the conflict node asa 2 The degrees of freedom of the left adjacent node and the right adjacent node of the conflict node in the transverse direction are respectivelya 1 、a 3 The degrees of freedom of the conflicting nodes satisfy the interpolation constraint of the following relation (3):
（3）。
the combining matrix can be penalty-functionalConversion to a second combining matrix->：
。
The penalty function can be solved by introducing a solution that is much larger thanK i，j (matrix)The value of any node) of the second combination matrix, and obtaining the value of the corresponding degree of freedom.
And S7, splicing the second combination matrixes of different interdigital structures according to the geometric structures to obtain an overall matrix of the filter device, calculating a frequency response curve of the filter device based on the overall matrix, and outputting the frequency response curve as a simulation result.
The invention has the beneficial effects that the invention provides a method for modeling the grid type by adopting the matching of high-order units and low-order units in the filter device simulation based on the finite element method, units with different orders are assembled in the model, and the conflict nodes in the high-order units are restrained and the degree of freedom of the conflict nodes is eliminated by utilizing the interpolation characteristic of the low-order units, so that the overall degree of freedom of the filter device model constructed by simulation is reduced on the premise of ensuring the calculation precision, the calculation dimension is reduced, and the overall calculation efficiency of the simulation process is improved.
Referring to fig. 7, fig. 7 is a schematic structural diagram of a finite element simulation system of mixed unit order provided in the embodiment of the present invention, where the finite element simulation system 200 is used for simulating a filter device based on a finite element method, and includes:
a geometry acquisition module 201, configured to acquire a geometry of the filter device;
the geometry differentiating module 202 is configured to split the filter device into a plurality of interdigital structures according to the geometry and the positions of the electrode metals, where the interdigital structures are divided into a first wavelength region and a second wavelength region according to the performance of the wavelength of the elastic wave;
a grid dividing module 203, configured to divide the first wavelength region into a plurality of first grids, and divide the second wavelength region into a plurality of second grids;
the finite element modeling module 204 is configured to model each first grid by using a preset higher-order unit based on a finite element method, so as to obtain a corresponding higher-order matrix; simultaneously, modeling each second grid by adopting a preset low-order unit to obtain a corresponding low-order matrix; wherein, the preset high-order unit and the preset low-order unit have different unit orders;
the finite element splicing module 205 is configured to splice the high-order matrix and the low-order matrix according to the positions of the first wavelength region and the second wavelength region to obtain a combined matrix of the finger inserting structure, where the splice positions of the high-order matrix and the low-order matrix have collision nodes with non-coincident transverse coordinates;
the constraint module 206 is configured to constrain the conflict nodes in the combination matrix by using a preset numerical constraint method, so as to obtain a second combination matrix;
and the output module 207 is configured to splice the second combination matrices of the different finger structures according to the geometric structure, obtain an overall matrix of the filter device, calculate a frequency response curve of the filter device based on the overall matrix, and output the frequency response curve as a simulation result.
Still further, the finite element splicing module 205 is specifically configured to:
acquiring the higher-order unit orders of the preset higher-order units and the lower-order unit orders of the preset lower-order units, and calculating the number of conflict nodes according to the higher-order unit orders and the lower-order unit orders;
acquiring the transverse coordinates of each conflict node, and constructing an interpolation expression for calculating the degree of freedom of the node in the preset low-order unit according to the low-order unit orders;
substituting the coordinates of each conflict node into the interpolation polynomials respectively for calculation to obtain the degree of freedom of the conflict node;
and combining the degrees of freedom of all the conflict nodes into the preset low-order unit for calculation to obtain the combination matrix.
The finite element simulation system 200 of the hybrid unit order can implement the steps in the finite element simulation method of the hybrid unit order in the above embodiment, and can achieve the same technical effects, which are not described herein again with reference to the description in the above embodiment.
Referring to fig. 8, fig. 8 is a schematic structural diagram of a computer device according to an embodiment of the present invention, where the computer device 300 includes: a memory 302, a processor 301 and a computer program stored on the memory 302 and executable on the processor 301.
The processor 301 invokes the computer program stored in the memory 302 to execute the steps in the finite element simulation method for mixed unit order provided in the embodiment of the present invention, please refer to fig. 2, specifically including the following steps:
s1, acquiring the geometric structure of the filter device.
S2, splitting the filter device into a plurality of interdigital structures according to the positions of electrode metals according to the geometric structures, wherein the interdigital structures are divided into a first wavelength region and a second wavelength region according to the wavelength performance of elastic waves.
S3, dividing the first wavelength region into a plurality of first grids, and dividing the second wavelength region into a plurality of second grids.
Further, the first grid has a different concentration in the first wavelength region than the second grid has in the second wavelength region.
S4, modeling each first grid by adopting a preset high-order unit based on a finite element method to obtain a corresponding high-order matrix; simultaneously, modeling each second grid by adopting a preset low-order unit to obtain a corresponding low-order matrix; the preset high-order unit and the preset low-order unit have different unit orders.
And S5, splicing the high-order matrix and the low-order matrix according to the positions of the first wavelength region and the second wavelength region to obtain a combined matrix of the interdigital structure, wherein the splicing positions of the high-order matrix and the low-order matrix are provided with conflict nodes with non-coincident transverse coordinates.
Still further, step S5 comprises the sub-steps of:
acquiring the higher-order unit orders of the preset higher-order units and the lower-order unit orders of the preset lower-order units, and calculating the number of conflict nodes according to the higher-order unit orders and the lower-order unit orders;
acquiring the transverse coordinates of each conflict node, and constructing an interpolation expression for calculating the degree of freedom of the node in the preset low-order unit according to the low-order unit orders;
substituting the coordinates of each conflict node into the interpolation polynomials respectively for calculation to obtain the degree of freedom of the conflict node;
and combining the degrees of freedom of all the conflict nodes into the preset low-order unit for calculation to obtain the combination matrix.
Still further, the interpolation expression satisfies the following relational expression (1):
（1）；
and:
（2）；
in the relational expressions (1) and (2),nthe number of orders of the cells is indicated,kis a node in the preset low-order unit, and1≤k≤n+ 1，xrepresenting the lateral coordinates of the nodes in the preset low-order cell,ythe degree of freedom of the node in the preset low-order unit is valued,P n+1 (x)representing the unit order asnThe transverse coordinates in the preset low-order unit are as followsxIs a node of the first class.
S6, restraining the conflict nodes in the combination matrix by adopting a preset numerical value restraining method to obtain a second combination matrix.
Further, the preset numerical constraint method is a penalty function method.
Further, the degrees of freedom of the conflicting nodes are defined asa 2 The degrees of freedom of the left adjacent node and the right adjacent node of the conflict node in the transverse direction are respectivelya 1 、a 3 The degrees of freedom of the conflicting nodes satisfy the interpolation constraint of the following relation (3):
（3）。
and S7, splicing the second combination matrixes of different interdigital structures according to the geometric structures to obtain an overall matrix of the filter device, calculating a frequency response curve of the filter device based on the overall matrix, and outputting the frequency response curve as a simulation result.
The computer device 300 provided in the embodiment of the present invention can implement the steps in the finite element simulation method of the mixed unit order in the above embodiment, and can implement the same technical effects, and is not described herein again with reference to the description in the above embodiment.
The embodiment of the invention also provides a computer readable storage medium, on which a computer program is stored, which when executed by a processor, implements each process and step in the method provided by the embodiment of the invention, and can implement the same technical effects, so that repetition is avoided, and no further description is provided herein.
Those skilled in the art will appreciate that implementing all or part of the above-described methods in accordance with the embodiments may be accomplished by way of a computer program stored on a computer readable storage medium, which when executed may comprise the steps of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM) or the like.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
From the above description of the embodiments, it will be clear to those skilled in the art that the above-described embodiment method may be implemented by means of software plus a necessary general hardware platform, but of course may also be implemented by means of hardware, but in many cases the former is a preferred embodiment. Based on such understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art in the form of a software product stored in a storage medium (e.g. ROM/RAM, magnetic disk, optical disk) comprising instructions for causing a terminal (which may be a mobile phone, a computer, a server, an air conditioner, or a network device, etc.) to perform the method according to the embodiments of the present invention.
While the embodiments of the present invention have been illustrated and described in connection with the drawings, what is presently considered to be the most practical and preferred embodiments of the invention, it is to be understood that the invention is not limited to the disclosed embodiments, but on the contrary, is intended to cover various equivalent modifications and equivalent arrangements included within the spirit and scope of the appended claims.
Claims (7)
1. A finite element simulation method of mixed unit order, the finite element simulation method being used for simulation of a filter device based on a finite element method, characterized in that the finite element simulation method comprises the steps of:
s1, acquiring the geometric structure of the filter device;
s2, splitting the filter device into a plurality of interdigital structures according to the positions of electrode metals according to the geometric structures, wherein the interdigital structures are divided into a first wavelength region and a second wavelength region according to the wavelength performance of elastic waves;
s3, dividing the first wavelength region into a plurality of first grids, and dividing the second wavelength region into a plurality of second grids;
s4, modeling each first grid by adopting a preset high-order unit based on a finite element method to obtain a corresponding high-order matrix; simultaneously, modeling each second grid by adopting a preset low-order unit to obtain a corresponding low-order matrix; wherein, the preset high-order unit and the preset low-order unit have different unit orders;
s5, splicing the high-order matrix and the low-order matrix according to the positions of the first wavelength region and the second wavelength region to obtain a combined matrix of the interdigital structure, wherein the splicing positions of the high-order matrix and the low-order matrix are provided with conflict nodes with non-coincident transverse coordinates;
s6, restraining the conflict nodes in the combination matrix by adopting a preset numerical constraint method to obtain a second combination matrix;
s7, splicing the second combination matrixes of different interdigital structures according to the geometric structures to obtain an overall matrix of the filter device, calculating a frequency response curve of the filter device based on the overall matrix, and outputting the frequency response curve as a simulation result;
wherein step S5 comprises the sub-steps of:
acquiring the higher-order unit orders of the preset higher-order units and the lower-order unit orders of the preset lower-order units, and calculating the number of conflict nodes according to the higher-order unit orders and the lower-order unit orders;
acquiring the transverse coordinates of each conflict node, and constructing an interpolation expression for calculating the degree of freedom of the node in the preset low-order unit according to the low-order unit orders;
substituting the coordinates of each conflict node into the interpolation polynomials respectively for calculation to obtain the degree of freedom of the conflict node;
combining the degrees of freedom of all the conflict nodes into the preset low-order unit for calculation to obtain the combination matrix;
the interpolation expression satisfies the following relation (1):
（1）；
and:
（2）；
in the relational expressions (1) and (2),nthe number of orders of the cells is indicated,kis a node in the preset low-order unit, and1≤k≤n+1，xrepresenting the lateral coordinates of the nodes in the preset low-order cell,ythe degree of freedom of the node in the preset low-order unit is valued,P n+1 (x)representing the unit order asnThe transverse coordinates in the preset low-order unit are as followsxIs a node of the first class.
2. The finite element simulation method of the mixed unit order according to claim 1, wherein the preset numerical constraint method is a penalty function method.
3. The finite element simulation method of the mixed unit order of claim 1, wherein the degrees of freedom defining the collision node isa 2 The degrees of freedom of the left adjacent node and the right adjacent node of the conflict node in the transverse direction are respectivelya 1 、a 3 The degrees of freedom of the conflicting nodes satisfy the interpolation constraint of the following relation (3):
（3）。
4. the finite element simulation method of the order of the hybrid unit according to claim 1, wherein the density of the first grid in the first wavelength region is different from the density of the second grid in the second wavelength region.
5. A finite element simulation system of mixed unit order for simulation of a filter device based on a finite element method, the finite element simulation system comprising:
the geometric acquisition module is used for acquiring the geometric structure of the filter device;
the geometrical difference module is used for dividing the filter device into a plurality of interdigital structures according to the geometrical structure and the positions of electrode metals, and the interdigital structures are divided into a first wavelength region and a second wavelength region according to the wavelength performance of elastic waves;
the grid dividing module is used for dividing the first wavelength region into a plurality of first grids and dividing the second wavelength region into a plurality of second grids;
the finite element modeling module is used for modeling each first grid by adopting a preset high-order unit based on a finite element method to obtain a corresponding high-order matrix; simultaneously, modeling each second grid by adopting a preset low-order unit to obtain a corresponding low-order matrix; wherein, the preset high-order unit and the preset low-order unit have different unit orders;
the finite element splicing module is used for splicing the high-order matrix and the low-order matrix according to the positions of the first wavelength region and the second wavelength region to obtain a combined matrix of the interdigital structure, wherein the splicing position of the high-order matrix and the low-order matrix is provided with a conflict node with non-coincident transverse coordinates;
the constraint module is used for constraining the conflict nodes in the combination matrix by adopting a preset numerical constraint method to obtain a second combination matrix;
the output module is used for splicing the second combination matrixes of different interdigital structures according to the geometric structures to obtain an overall matrix of the filter device, calculating a frequency response curve of the filter device based on the overall matrix, and outputting the frequency response curve as a simulation result;
the finite element splicing module is specifically used for:
acquiring the higher-order unit orders of the preset higher-order units and the lower-order unit orders of the preset lower-order units, and calculating the number of conflict nodes according to the higher-order unit orders and the lower-order unit orders;
acquiring the transverse coordinates of each conflict node, and constructing an interpolation expression for calculating the degree of freedom of the node in the preset low-order unit according to the low-order unit orders;
substituting the coordinates of each conflict node into the interpolation polynomials respectively for calculation to obtain the degree of freedom of the conflict node;
combining the degrees of freedom of all the conflict nodes into the preset low-order unit for calculation to obtain the combination matrix;
the interpolation expression satisfies the following relation (1):
（1）；
and:
（2）；
in the relational expressions (1) and (2),nthe number of orders of the cells is indicated,kis a node in the preset low-order unit, and1≤k≤n+1，xrepresenting the lateral coordinates of the nodes in the preset low-order cell,ythe degree of freedom of the node in the preset low-order unit is valued,P n+1 (x)representing the unit order asnThe transverse coordinates in the preset low-order unit are as followsxIs a node of the first class.
6. A computer device, comprising: memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps in the mixed-element-order finite element simulation method according to any of claims 1-4 when the computer program is executed.
7. A computer readable storage medium, characterized in that the computer readable storage medium has stored thereon a computer program which, when executed by a processor, implements the steps of the finite element simulation method of the hybrid cell order of any of claims 1-4.
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