CN108072899B - Self-adaptive implementation method of discontinuous Galerkin finite element seismic numerical simulation algorithm - Google Patents
Self-adaptive implementation method of discontinuous Galerkin finite element seismic numerical simulation algorithm Download PDFInfo
- Publication number
- CN108072899B CN108072899B CN201610987996.9A CN201610987996A CN108072899B CN 108072899 B CN108072899 B CN 108072899B CN 201610987996 A CN201610987996 A CN 201610987996A CN 108072899 B CN108072899 B CN 108072899B
- Authority
- CN
- China
- Prior art keywords
- order
- finite element
- units
- adjacent
- unit
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 41
- 238000004422 calculation algorithm Methods 0.000 title claims abstract description 16
- 238000004088 simulation Methods 0.000 claims abstract description 41
- 238000013507 mapping Methods 0.000 claims abstract description 20
- 238000004364 calculation method Methods 0.000 claims abstract description 17
- 239000011159 matrix material Substances 0.000 claims abstract description 17
- 230000004907 flux Effects 0.000 claims abstract description 4
- 230000003044 adaptive effect Effects 0.000 claims description 9
- 230000014509 gene expression Effects 0.000 claims description 5
- 238000012216 screening Methods 0.000 claims description 2
- 230000000694 effects Effects 0.000 description 6
- 238000010586 diagram Methods 0.000 description 5
- 230000008859 change Effects 0.000 description 3
- 238000012545 processing Methods 0.000 description 2
- 238000005070 sampling Methods 0.000 description 2
- 230000006978 adaptation Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 238000012937 correction Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 230000004069 differentiation Effects 0.000 description 1
- 239000006185 dispersion Substances 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000010354 integration Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000008569 process Effects 0.000 description 1
- 230000003068 static effect Effects 0.000 description 1
- 239000000126 substance Substances 0.000 description 1
- 238000012876 topography Methods 0.000 description 1
- 230000037303 wrinkles Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. for interpretation or for event detection
- G01V1/36—Effecting static or dynamic corrections on records, e.g. correcting spread; Correlating seismic signals; Eliminating effects of unwanted energy
- G01V1/362—Effecting static or dynamic corrections; Stacking
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V2210/00—Details of seismic processing or analysis
- G01V2210/50—Corrections or adjustments related to wave propagation
- G01V2210/53—Statics correction, e.g. weathering layer or transformation to a datum
Landscapes
- Engineering & Computer Science (AREA)
- Remote Sensing (AREA)
- Physics & Mathematics (AREA)
- Life Sciences & Earth Sciences (AREA)
- Acoustics & Sound (AREA)
- Environmental & Geological Engineering (AREA)
- Geology (AREA)
- General Life Sciences & Earth Sciences (AREA)
- General Physics & Mathematics (AREA)
- Geophysics (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
A self-adaptive realization method of an interrupted Galerkin finite element seismic numerical simulation algorithm comprises the following steps: firstly, defining mesh generation density, and performing non-structural mesh generation on a calculation area according to the mesh density; secondly, determining the polynomial expansion order p on each grid unit; decoupling two adjacent grid units, and selecting a proper numerical value flux format as a wave field exchange mode between the adjacent grid units; digitizing the decoupling equation to obtain a space discrete equation on each grid unit; fifthly, solving an inner product between wave field functions on a common boundary of two adjacent units to obtain an edge value mapping matrix; selecting a proper time integral format; and seventhly, mapping the wave fields of the adjacent units with different orders by using the edge value mapping matrix, calculating a space discrete part, applying a seismic source condition, updating the wave field component, and obtaining a simulation result.
Description
Technical Field
The invention relates to a seismic wave field numerical simulation technology applied to complex earth surfaces and complex structures, in particular to a finite element numerical solving algorithm.
Background
At present, in southern and western regions of China, the emphasis of oil-gas seismic exploration is turning to complex regions such as hills and pre-mountain construction zones. In the regions, the surface conditions are abnormally complex, the topography fluctuation is severe, the altitude difference change is very large, the near-surface structure nonuniformity is severe due to large lithologic speed change, and meanwhile, the underground structure is complex, such as strong wrinkles, fault development, steep structure, large stratum change and the like. They cause problems in such areas, such as low signal-to-noise ratio of seismic data and difficult static correction. Fundamentally solves these exploration problems, needs to deeply know the propagation law and wave field characteristics of seismic waves under the condition of undulating surface, and the finite element method is the most effective technical means for carrying out numerical simulation of seismic waves in complex surface and complex structure areas.
The Discontinuous Galerkin Finite Element Method (DGFEM) is a high-order finite element method. DG-FEM based on numerical flow theory is essentially the combination of finite element method and finite body method, the finite element method is used for processing in the unit, the processing idea of numerical flow in the finite body method is adopted on the unit boundary, therefore, the method inherits the advantages of high order of the finite element method, local characteristics of the finite body method and the like, simultaneously overcomes some defects of the two methods, and can realize high-precision, low-frequency dispersion and effective numerical simulation. The method can use non-structural grid units (including triangular or tetrahedral grids) and can design an optimal grid according to the distribution characteristics of a medium, so that the discontinuous Galerkin finite element method is particularly suitable for the seismic wave propagation numerical simulation under the conditions of undulating surfaces and complex structures.
Due to the characteristics of high-order convergence and the like of the DG-FEM, when a general explicit time format is adopted, the requirement on the time step is strict, for example, in the Rongo Kutta time format, the step is reduced by the proportion of 1/(2p +1) along with the increase of the spatial order p. In addition, when the finite element mesh is used for finely dividing the underground medium model, a small mesh high-speed body unit is inevitably generated, and the limitation on the step length is more prominent according to the CFL stability condition. When a local dense grid exists in the model, although most of regional grid units are large, when a global time step is adopted, the global time step is small in order to meet the strict time step of the local dense grid, so that the efficiency of the whole simulation calculation is severely limited.
A common way to overcome the step size limitation of explicit time formats is to use implicit time formats, but generally implicit time formats require inversion of large-scale sparse matrices, which is not an easy task. For simulating elastic wave propagation by using DG-FEM in practice, even if sparse storage is adopted, storage of a dispersed large sparse matrix is difficult to bear, and the method is more prominent in a three-dimensional situation. Another preferred method is to use local time steps, but this is relatively complicated to accomplish.
The low order method allows for a larger time step to be used than the high order discontinuous Galerkin finite element method. The discontinuous Galerkin finite element method has good local characteristics, the solution of which depends on unit by unit, allows each unit to select independent spatial orders for calculation, so that it can be considered to use low-order simulation for units with stricter time step size limitation, and to use high-order simulation for other units to guarantee simulation accuracy, so-called order adaptation or p-adaptation.
Disclosure of Invention
Aiming at the problem that a small global time step length is caused by a local small grid unit or a malformed unit in a model when the earthquake wave propagation numerical simulation is carried out by using an interrupted Galerkin finite element method (LF-DG), the p-adaptive algorithm is realized by using the local characteristic of the interrupted Galerkin finite element method, each unit is allowed to set an independent space order, the optimized local time step length is further obtained, and the simulation calculation efficiency is improved.
The purpose of the invention and the technical problem to be solved are realized by adopting the following technical scheme.
The method comprises the following steps:
(1) defining mesh generation density, and performing non-structural mesh generation on the calculation area according to the mesh generation density;
(2) determining a polynomial expansion order p on each grid cell;
(3) decoupling two adjacent grid units, and selecting a proper numerical value flux format as an inter-adjacent-unit wave field exchange mode;
(4) digitizing the decoupling equation to obtain a space discrete equation on each grid unit;
(5) solving an inner product between wave field functions on a common boundary of two adjacent units to obtain an edge value mapping matrix;
(6) selecting a proper time integration format;
(7) and mapping adjacent unit wave fields with different orders by using the edge value mapping matrix, calculating a space discrete part, applying a seismic source condition, updating wave field components and obtaining a simulation result.
Wherein the step (2) is obtained by the following steps:
(1) inputting a simulation time step dt and a maximum simulation order pmax;
(2) determining a stability condition number CFL (p) of each stage of algorithm;
(3) calculating a time step standard of each unit;
(4) calculating the stability condition of each unit k under pmax;
(5) adopting pmax order for all units with dtk being more than or equal to dt;
(6) repeating the steps (4) and (5) in sequence, and screening out calculation units with orders pmax-1 and pmax-2 … in sequence;
(7) when all cells do not obtain a certain calculation order, it is prompted to reduce the analog time step size dt.
The step (5) is obtained by the following steps:
(1) mapping the functions of two adjacent cells to the cell boundary, and setting them on the boundary to be composed of two groups of orthogonal mode spaces with different orders
To represent
(2) Deriving functions for different order expansions
The inner product at the boundary is represented as
(3) Representing inner product of function on cell boundary by using modal space coordinate of function on cell and boundary integral operator
The time integral format is a Longgonkuta time format and a frog leaping time format.
The numerical value stream is a central numerical value stream and a local Lax-Friedrich.
Step (2) whereinmnThe expression dimension is (p)m+1)*(pn+1) identity matrix.
Wherein
The physical space coordinates of the function on the boundary can be represented by the modal space coordinates of the function on the cell as
Wherein the inner product of the boundary operator
Edge value mapping matrix
When all cells do not obtain a certain calculation order, it is prompted to reduce the analog time step size dt.
The invention has the following advantages and beneficial effects: the method is suitable for high-precision and high-efficiency numerical simulation of seismic wave propagation in complex conditions (particularly severe topographic relief and the like), realizes a p self-adaptive algorithm by utilizing the local characteristics of an interrupted Galerkin finite element method, allows each unit to set an independent space order, further obtains an optimized local time step length, and improves the simulation calculation efficiency. The invention has novel theory and strong technical process practicability and is suitable for wide application in the industry.
Drawings
The invention will be described in more detail hereinafter on the basis of embodiments and with reference to the accompanying drawings. Wherein:
FIG. 1 is a schematic diagram of a homogeneous model and its mesh distribution
FIG. 2(a) is a spatial order distribution diagram
FIG. 2(b) is a graph showing the effect of the p-adaptive simulation result when the time step dt is 0.20ms
FIG. 2(c) is a graph of the effect of difference of single-order simulation results when the time step dt is 0.20ms
FIG. 3(a) is a spatial order distribution diagram
FIG. 3(b) is a graph showing the effect of the p-adaptive simulation result when the time step dt is 0.25ms
FIG. 3(c) is a graph of the effect of difference of single-order simulation results when the time step dt is 0.25ms
FIG. 4(a) is a spatial order distribution diagram
FIG. 4(b) is a graph showing the effect of the p-adaptive simulation result when the time step dt is 0.40ms
FIG. 4(c) is a graph of the effect of difference of single-order simulation results when the time step dt is 0.40ms
FIG. 5 is a table of L2 error versus computational efficiency
In the drawings, like parts are provided with like reference numerals. The drawings are not to scale.
Detailed Description
The invention will be further explained with reference to the drawings.
Aiming at the problem that a small global time step is caused by a local small grid unit or a malformed unit in a model when the intermittent Galerkin finite element method is used for carrying out seismic wave propagation numerical simulation, the invention skillfully applies a mode of solving the internal product by a distribution point differentiation method by rechecking the internal product of wave field functions of two different orders on the same integral region (cell boundary), skillfully deduces a mapping matrix between unfolded wave fields of different orders, realizes p-adaptive simulation, provides a method for setting independent space polynomial unfolding orders for each unit, further obtains an optimized local time step and improves the simulation calculation efficiency. The method comprises the following specific steps:
defining a grid density function according to the model velocity distribution and the space sampling requirement of the seismic wave finite element method
Wherein v issIs the transverse wave velocity, fmaxFor the maximum frequency of the wavelets used in the simulation, N represents the number of sampling points required within a shortest transverse wave wavelength, and when a spatial second order is adopted, N is 1.9, and when a spatial third order is adopted, N is 0.9.
Inputting analog calculation time step length and the adopted maximum space order pMAX, and setting the most appropriate space polynomial expansion order on each unit according to the analog stability criterion.
And (3) deriving an integral equation (finite element equation) corresponding to an elastic wave first-order velocity-stress equation by using the basic principle of an interrupted Galerkin finite element method to realize the decoupling of adjacent grid units, wherein a proper numerical flow is selected as a wave field exchange mode between the adjacent units, such as central numerical flow, local Lax-Friedrich and the like.
And digitizing the decoupling integral equation by adopting a mode of solving the inner product by a distribution point differential method to obtain a space discrete equation on each unit. The p-adaptation algorithm allows each cell to employ an independent spatial polynomial expansion order. Only when the inner product term of the wave field function on the cell boundary is solved, the space order adopted by the adjacent cell can influence the calculation of the wave field of the cell, and the calculation of other volume integral terms is only related to the selection of the space order of the cell, so that the inner product of the wave field function on the common boundary of the two adjacent cells is mainly considered and expressed as
Wherein the content of the first and second substances,
are respectively defined in adjacent units omegam、ΩnHaving a common boundary
The two units adopt independent space orders which are respectively pmAnd pn. Firstly, mapping functions to unit boundaries, and setting the functions to be composed of two groups of orthogonal modal spaces with different orders on the boundaries
To represent
Deriving functions for different order expansions
Inner product representation on boundary
Wherein, ImnThe expression dimension is (p)m+1)*(pn+1) identity matrix. From the mapping relationship between the mode space and the physical space on the boundary, there is
In addition, from the whole unit, the physical space coordinate of the boundary of the function can be represented by the modal space coordinate of the function on the unit
The above two groups of expressions are combined
Finally, the inner product of the function on the cell boundary can be represented by the modal space coordinates of the function on the cell and the boundary integral operator (here, directly expressed in the form of a node in the expression <2-40 >)
Wherein, the boundary inner product operator
Edge value mapping matrix
Obviously the unit omegamBoundary inner product operator S 'of'keRelying only on the and unit omegamAdopted byThe space order Pm is only needed to map the wave field values on the boundary of the adjacent units to a matrix T according to the edge values before calculating the wave field jump of the two edges of the boundarymnAnd realizing interpolation.
And selecting a proper time integral format, such as a Longgonkuta time format, a frog leaping time format and the like.
Using a mapping matrix TmnMapping adjacent unit wave fields of different orders, calculating space discrete part, applying seismic source condition, updating wave field component and obtaining final simulation result.
Example (b):
FIG. 1 is a schematic diagram of a homogeneous model and a grid distribution case;
the model was simulated using an algorithm of order P3. In order to meet the requirement of the global grid on stability, the time step dt is less than or equal to 0.11ms, and a simulation time step of 0.1ms is adopted. When the simulation is performed with a time step dt of 0.2ms, it can be seen from fig. 2 that in order to meet the stability requirement, a small number of cells at the local grid encryption site need to be calculated by using a p2 order cell, and other regions are still simulated by using a p3 order cell, where fig. 2(b) is a p adaptive simulation result, and fig. 2(c) is a difference between the p adaptive simulation result and a single p3 order simulation result. Comparing the magnitude of the values, the peak of the simulation results reached 4 × 104, and the peak of the difference was 1000, i.e., the difference was about 2-5%.
When dt is 0.25ms in fig. 3, more cells at local trellis stage encryption need to use p2 order simulation. The difference from a single p3 order simulation is about 3-7.5%.
In fig. 4, when dt is 0.4ms, most cells in the local trellis encryption need to be simulated by p1-p2, and some cells in other regions of the model need to be simulated by p 2. The difference from a single p3 order simulation is about 7.5%.
From fig. 5, it can be seen that the p-adaptive algorithm can meet the accuracy requirement and obviously improve the calculation efficiency by increasing the simulation time step length.
While the invention has been described with reference to a preferred embodiment, various modifications may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In particular, the technical features mentioned in the embodiments can be combined in any way as long as there is no structural conflict. It is intended that the invention not be limited to the particular embodiments disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.
Claims (5)
1. An adaptive implementation method for an intermittent Galerkin finite element seismic numerical simulation algorithm is characterized by comprising the following steps of:
firstly, defining mesh generation density, and performing non-structural mesh generation on a calculation area according to the mesh generation density;
secondly, determining the polynomial expansion order p on each grid unit;
decoupling two adjacent grid units, and selecting a proper numerical value flux format as a wave field exchange mode between the adjacent grid units, wherein the numerical value flux format is a central numerical value flow or a local Lax-Friedrich numerical value flow;
digitizing the decoupling equation to obtain a space discrete equation on each grid unit;
fifthly, solving an inner product between wave field functions on a common boundary of two adjacent units to obtain an edge value mapping matrix;
selecting a proper time integral format, wherein the time integral format is a Longgongkuta time format or a frog leaping time format;
mapping adjacent unit wave fields of different orders by using the edge value mapping matrix, calculating a space discrete part, applying a seismic source condition, updating wave field components and obtaining a simulation result;
wherein, the second step is obtained by the following steps:
(1) inputting a simulation time step dt and a maximum simulation order pmax;
(2) determining a stability condition number CFL (p) of each stage of algorithm;
(3) calculating a time step standard of each unit;
(4) calculating the stability condition of each unit k under the maximum simulation order pmax;
(5) adopting a maximum analog order pmax order for all units with dtk being more than or equal to dt;
(6) and (5) repeating the steps (4) and (5) in sequence, and screening out the calculation units with the orders of pmax-1 and pmax-2 … in sequence.
2. The adaptive realization method of an interrupted Galerkin finite element seismic numerical simulation algorithm according to claim 1, wherein the fifth step is obtained by the following steps:
mapping functions of two adjacent cells to cell boundaries, and setting the functions on the boundaries to be composed of two groups of orthogonal mode spaces with different orders
To represent
II deducing functions expanded by different orders
The inner product at the boundary is represented as
III using the mode space coordinate of the function on the cell and the boundary integral operator to express the inner product of the function on the cell boundary
pmAnd pnThe spatial order of two adjacent units respectively,
are respectively defined in adjacent units omegam、ΩnWave field function ofmnThe expression dimension is (p)m+1)*(pnA unit matrix of + 1); s'keAs an inner product of boundaries, TmnMapping a matrix for the edge values; wherein the inner product of the boundary operator
Edge value mapping matrix
3. The adaptive realization method of discontinuous Galerkin finite element seismic numerical simulation algorithm according to claim 2, wherein, the adaptive realization method is characterized in that
4. The adaptive realization method of discontinuous Galerkin finite element seismic numerical simulation algorithm according to claim 2, wherein the physical space coordinates of the function on the boundary are represented by the modal space coordinates of the function on the unit as
5. The adaptive implementation method of the intermittent Galerkin finite element seismic numerical simulation algorithm according to claim 1, wherein the adaptive implementation method comprises the following steps: further comprising the step (7) of prompting a reduction of the analog time step size dt when all the cells have not obtained the determined calculation order.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610987996.9A CN108072899B (en) | 2016-11-10 | 2016-11-10 | Self-adaptive implementation method of discontinuous Galerkin finite element seismic numerical simulation algorithm |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610987996.9A CN108072899B (en) | 2016-11-10 | 2016-11-10 | Self-adaptive implementation method of discontinuous Galerkin finite element seismic numerical simulation algorithm |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN108072899A CN108072899A (en) | 2018-05-25 |
| CN108072899B true CN108072899B (en) | 2020-09-15 |
Family
ID=62154350
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201610987996.9A Active CN108072899B (en) | 2016-11-10 | 2016-11-10 | Self-adaptive implementation method of discontinuous Galerkin finite element seismic numerical simulation algorithm |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108072899B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110988993B (en) * | 2019-11-27 | 2021-01-26 | 清华大学 | Offset imaging method and device and electronic equipment |
Family Cites Families (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9529110B2 (en) * | 2008-03-31 | 2016-12-27 | Westerngeco L. L. C. | Constructing a reduced order model of an electromagnetic response in a subterranean structure |
| US8032304B2 (en) * | 2008-10-06 | 2011-10-04 | Chevron U.S.A. Inc. | System and method for deriving seismic wave fields using both ray-based and finite-element principles |
| CN103530451B (en) * | 2013-09-27 | 2016-09-28 | 中国科学院声学研究所 | Many grids Chebyshev parallel spectral element method of complex dielectrics elastic wave modeling |
| CN104951580B (en) * | 2014-03-28 | 2019-03-29 | 南京理工大学 | The time domain spectral element emi analysis method of unconditional stability and condition stability mixing |
| CN103970717B (en) * | 2014-05-08 | 2017-03-22 | 中国人民解放军理工大学 | Unconditional stability FDTD method based on Associated Hermite orthogonal function |
-
2016
- 2016-11-10 CN CN201610987996.9A patent/CN108072899B/en active Active
Also Published As
| Publication number | Publication date |
|---|---|
| CN108072899A (en) | 2018-05-25 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Ringler et al. | A multi-resolution approach to global ocean modeling | |
| Qian et al. | Fast sweeping methods for eikonal equations on triangular meshes | |
| CN105319581B (en) | A kind of efficient time-domain full waveform inversion method | |
| Paszyński et al. | A parallel direct solver for the self-adaptive hp Finite Element Method | |
| Nakahashi et al. | Building-cube method for large-scale, high resolution flow computations | |
| Minisini et al. | Local time stepping with the discontinuous Galerkin method for wave propagation in 3D heterogeneous media | |
| Lee et al. | Simple and efficient solution of the shallow water equations with source terms | |
| CN103630933A (en) | Nonlinear optimization based time-space domain staggered grid finite difference method and device | |
| Yang et al. | A simple Galerkin meshless method, the fragile points method using point stiffness matrices, for 2D linear elastic problems in complex domains with crack and rupture propagation | |
| CN111639429A (en) | Underwater sound field numerical simulation method, system and medium based on Chebyshev polynomial spectrum | |
| CN107657075B (en) | The Region Decomposition FInite Element of Darcy velocity at simulated groundwater dielectric interface | |
| Yue et al. | A multi‐grid method of high accuracy surface modeling and its validation | |
| Williamschen et al. | Parallel anisotropic block-based adaptive mesh refinement algorithm for three-dimensional flows | |
| CN111507026A (en) | Dual-grid multi-scale finite element method for simulating node Darcy permeation flow rate | |
| Ma et al. | Calculating Ray Paths for First‐Arrival Travel Times Using a Topography‐Dependent Eikonal Equation Solver | |
| Kuzmin et al. | Algebraic flux correction II. Compressible Euler equations | |
| Piggott et al. | Unstructured adaptive meshes for ocean modeling | |
| Wu et al. | A local solution approach for adaptive hierarchical refinement in isogeometric analysis | |
| Salehipour et al. | A higher order discontinuous Galerkin, global shallow water model: Global ocean tides and aquaplanet benchmarks | |
| CN108072899B (en) | Self-adaptive implementation method of discontinuous Galerkin finite element seismic numerical simulation algorithm | |
| Adcroft | Numerical algorithms for use in a dynamical model of the ocean | |
| CN105974471A (en) | Seismic data multi-GPU fast forward computation method based on asynchronous flow | |
| Fu et al. | Multiscale modeling of acoustic wave propagation in 2D heterogeneous media using local spectral basis functions | |
| Restrepo et al. | Virtual topography: A fictitious domain approach for analyzing free‐surface irregularities in large‐scale earthquake ground motion simulation | |
| CN103425881A (en) | Method for certainty numerical simulation of crack medium seismic wave response |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |