CN105589678A - Time domain finite-difference method implemented by using digital signal processing technique - Google Patents
Time domain finite-difference method implemented by using digital signal processing technique Download PDFInfo
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- CN105589678A CN105589678A CN201410567636.4A CN201410567636A CN105589678A CN 105589678 A CN105589678 A CN 105589678A CN 201410567636 A CN201410567636 A CN 201410567636A CN 105589678 A CN105589678 A CN 105589678A
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Abstract
The invention proposes a time domain finite-difference method implemented by using a digital signal processing technique, which is used for the field of design and application of electromagnetic field software. A Courant-Friendrich-Levy time stability condition can be broken through by using the time domain finite-difference method with a hidden alternative direction; in order to simplify the whole electromagnetic calculation process, matrixes and vectors in a hidden time domain finite-difference equation are arranged according to the requirement of digital signal processing, and a discrete difference equation is pre-processed; and for a parallel technology, the time domain finite-difference method with the hidden alternative direction is completed by combining the digital signal processing technique according to a time discrete signal flow chart so as to calculate an electromagnetic field numerical value. With the method proposed by the invention, the electromagnetic field calculation efficiency can be improved; compared with a traditional time domain finite-difference method, the method has the advantages that a Courant-Friendrich-Levy (CFL) factor is appropriately selected, and the calculation efficiency can be improved by 3 to 5 times; and moreover, the method proposed by the invention can be effectively combined with a telescopic coordinate completely-matching layer, unbounded transmission of simulated electromagnetic wave can be achieved, and the method can be more widely applied.
Description
Technical field
The invention belongs to and calculate electromagnetism software technology field, relate to and a kind ofly the Finite Difference-Time Domain separating method of alternating direction implicit is carried out to pretreatment with Digital Signal Processing, improved computational efficiency.
Background technology
Finite Difference-Time Domain separating method is to calculate one of computational methods that electromagnetism is conventional. In time and spatial domain, Maxwell equation group is carried out to direct differential discrete, simulate electromagnetic communication process. This method has been applied among the researchs such as microwave circuit, antenna and Electromagnetic Scattering of Target. Traditional method is limited to Courant-Friedrich-Levy (CFL) time stability condition:, necessarily require the CFL factor to be less than or equal to 1, i.e. time step ΔtBe limited to the size of space minimum grid. Therefore while having small structure on analysis large sized object, mesh generation is just thinner, and computing time is just longer. In 1999, Namiki and Zheng proposed respectively the Finite Difference-Time Domain separating method of alternating direction implicit, and this method has broken through the restriction of CFL condition. For the problem of labyrinth, increase sometimes its computing time.
Digital Signal Processing is a kind of technology of according to the form of presentation of numerical computations, signal being carried out suitably processing processing. Along with the fast development of computer technology, this technology extends among different scientific domains especially. Because Finite Difference-Time Domain separating method is that time-discrete electromagnetic field is sampled and calculated, meet the requirement of Digital Signal Processing to signal, if Digital Signal Processing is used for to complex electromagnetic fields numerical computations problem, especially time domain computational problem, discrete DIFFERENCE EQUATIONS is carried out to pretreatment, can improve the efficiency of electromagnetic-field simulation.
Summary of the invention
The present invention proposes a kind of Finite Difference-Time Domain separating method of realizing alternating direction implicit with Digital Signal Processing. DIFFERENCE EQUATIONS is carried out to pretreatment, can reduce further the complexity of algorithm, make full use of the computer's software resource of Digital Signal Processing, solved traditional method and had long drawback computing time, improve computational efficiency. It is characterized in that:
There is electromagnetism computational process twice in the Finite Difference-Time Domain separating method of alternating direction implicit, at this moment the time step of electric-field intensity is placed inn-1/2、n+ 1/2 HenIn+1 moment, the time step of magnetic field intensity is placed inn-1/4、n+1/4 HenIn+3/4 moment, because time step need to be processed through staggered, be not at this moment just limited to CFL time stability condition
(1)
So the desirable value that is greater than 1 of CFL, by the Finite Difference-Time Domain separating method of coefficient matrix form statement alternating direction implicit, two processes that obtain respectively it are
Process one:
(2)
(3)
Process two:
(4)
(5)
WhereinAWithBBe the component form of curl differentiating operator, it is expressed as
(6)
Because H n+1/4In process one, be all unknown quantity, will H n+1/4Substitution E n+1/2In go, and will E n+1/2All Xiang Jun be placed in the left side of equation, so have
(7)
Use the same method, can obtain the electric-field intensity expression of process two
(8)
The Finite Difference-Time Domain separating method that can sum up thus alternating direction implicit is the computational methods of discrete time-domain, in whole computational methods, and electric field E And magnetic field H Express their variablees in three directions with vector formE x ,E y ,E z WithH x ,H y ,H z They are all subject to the effect of other matrix operator, concentrating has used more general matrix algebra to represent form, make (2) and (7) of process one and (4) and (8) of process two all meet the expression form of system performance, determine that the Finite Difference-Time Domain separating method of alternating direction implicit can use matrix notation, so just met the pretreated basic demand of data signal. Above matrix and vector in various arranged according to the requirement of Digital Signal Processing, in order to simplify whole electromagnetism computational process, Fig. 1 has described the discretely-timed signal flow chart under the Finite Difference-Time Domain separating method of alternating direction implicit, has clearly reflected the basic process of this method. Digital signal technique pretreatment can be made clear and definite optimization to the concrete calculating of matrix and vector, thereby can further improve computational efficiency, reduces a large amount of unnecessary computing repeatedly, and has saved a large amount of computer resources. For concurrent technique, utilize the discretely-timed signal flow chart of Fig. 1, can more effectively realize the computational process of many Computer Resources Allocation.
For analog electrical magnetic wave is in the communication process of unbounded space, adopt the flexible complete matching layer of coordinate, need to be to (2), (3), (4) and (5) formula is modified, and obtains
(9)
(10)
(11)
(12)
WhereinA WithB Be the component form of curl differentiating operator, be expressed as
Further process and just can complete the numerical computations under this method by recursive convolution. In the time that 3-D geometric model carries out electromagnetism calculating,WithIn isotropic medium, be three matrix of strips, its inversion operation method has developed quite ripely in Digital Signal Processing, the representation of this sytem matrix has reflected its characteristics of signals in Fig. 1, is convenient to programming and the corresponding data processing of computer.
Compared with traditional Finite Difference-Time Domain separating method, suitably choose the CFL factor, the present invention, by after data signal pretreatment, can obviously improve the computational efficiency of 3 to 5 times; Can combine with the flexible complete matching layer of coordinate, realize the propagation of analog electrical magnetic wave at unbounded space, it is used widely; Can directly carry out the Electromagnetic Simulation designs such as low-frequency channel, microwave circuit, Antenna Design and target scattering.
Brief description of the drawings
Fig. 1 is the discretely-timed signal flow chart of the Finite Difference-Time Domain separating method of alternating direction implicit of the present invention;
Fig. 2 is the structure chart of the low frequency rlc circuit of the embodiment of the present invention;
Fig. 3 is that the electric capacity of low frequency rlc circuit and the time domain of inductance series voltage of the embodiment of the present invention distributes;
Fig. 4 is the transfer function analysis chart of the low frequency rlc circuit of the embodiment of the present invention;
Fig. 5 is the structure chart of the low pass filter of the embodiment of the present invention;
Fig. 6 is the reflectance factor of the low pass filter of the embodiment of the present inventionS 11Curve;
Fig. 7 is the transmission coefficient of the low pass filter of the embodiment of the present inventionS 21Curve;
Fig. 8 is the time domain distribution map of the dipole of the embodiment of the present invention;
Fig. 9 is the error map of the dipole of the embodiment of the present invention.
Detailed description of the invention
The present invention is a kind of Finite Difference-Time Domain separating method of realizing alternating direction implicit with data signal preforming technique, below in conjunction with concrete drawings and Examples, the present invention is made further and being explained, and the explanation of the invention is not limited.
Example 1. Fig. 2 have provided the schematic diagram of low frequency rlc circuit, utilize method of the present invention and traditional Finite Difference-Time Domain separating method, and the voltage time domain of calculating respectively it distributes and corresponding transfer function.
In order to realize, circuit is carried out to frequency-domain analysis, general employing modulation Gaussian pulse etc. is realized as driving source. ArrangeL=10nH inductance,CThe circuit of=10pF capacitances in series, and add internal resistance to beRThe voltage source excitation of=50 Ω, utilizes the method that the present invention proposes to carry out simulation calculation to this circuit, because the size of circuit is little, any absorbing boundary condition is not set on zoning, always calculates the size delta that area size is 9 × 9 × 9, Yee cellularx=Δy=Δz=1mm, the component (being inductance, electric capacity and resistance) of emulation all can be positioned on the center, zoning of Finite Difference-Time Domain separating method of alternating direction implicit, obtains the time domain of electric capacity and inductance series voltage after emulation and distributes and corresponding transfer function |T(ω) | analysis chart, respectively as shown in Figure 3 and Figure 4. Contrast with traditional Finite Difference-Time Domain separating method, in the time of CFL=6, adopt the preconditioning technique shown in Fig. 1 can improve the computational efficiency of 5 times of left and right, as shown in the table.
Upper table has reflected method of the present invention except not being limited to CFL time stability condition, and along with the increase of the CFL factor, the CPU of same computation model reduces running time again and again. According to Fig. 3 and Fig. 4, can find out that result of calculation almost fits like a glove.
Example 2. Fig. 5 have provided a kind of structure chart of microwave low-pass filter, utilize method of the present invention and traditional Finite Difference-Time Domain separating method, calculate respectively its reflectance factorS 11Curve and transmission coefficientS 21Curve.
This low-pass filter structure belongs to microwave circuit. Total size that zoning is set is 76 × 72 × 30, and the flexible complete matching layer of coordinate is set on cutoff boundary, and its border preset parameter is respectivelyn pml =3；σ factor =1.3；κ max=7；α max=7；α min=0; Add after the arranging of boundary condition, the structure of low pass filter is positioned over to the center of zoning, utilize the method that the present invention proposes to carry out Electromagnetic Simulation to this structure, obtain the reflectance factor of low pass filterS 11Curve and transmission coefficientS 21Curve, respectively as shown in Figure 6 and Figure 7. Obtain following form computing time simultaneously:
Upper table has shown the method for the discretely-timed signal flow chart that utilizes Fig. 1, and the Finite Difference-Time Domain separating method of alternating direction implicit is carried out after data signal preconditioning technique, can reduce computing time to the Electromagnetic Simulation process of microwave circuit, improves corresponding efficiency.
Example 3. is utilized method of the present invention and traditional Finite Difference-Time Domain separating method, calculates respectively dipole and at point of observation isr=10δ,θ=90 ° of electric fields of locating over time and error condition.
Dipole is in the radiation field of time domain
Current density because of what introduce in computational process, by dipole moment p With current density J Relation
Because it is square that Yee cellular as elementary cell, might as well be supposed Yee cellular, each length of side isδ, above formula can change into:
If dipole edgezDirection of principal axis vibration, and dipole is only by electric field componentE z Produce, utilize Maxwell's curl formula, can obtain the discrete scheme of Finite Difference-Time Domain separating method:
If dipole source is, whereinT=2ns, just can obtain point of observation and ber=10δ,θ=90 ° of radiation fields of locatingE z Distribution situation. If the square length of side of each Yee cellular is Δx=Δy=Δz=δ=5cm, whole zoning size is 50 × 50 × 50, and the flexible complete matching layer of 8 layers of coordinate is set on zoning, its parameter arranges as example 2, radiation source is arranged on to the center (25,25,25) of whole electromagnetism zoning, point of observation (15,25,25) soE z Distribution of results isr=10δ,θ=90 ° of electric-field intensity of locatingE z , its time dependent simulation result as shown in Figure 8, compares with analysis result, and error result is as shown in Figure 9. Computing time and computational efficiency are as shown in the table.
By the preprocessing process of Fig. 1, upper table has reflected that method of the present invention can effectively reduce the CPU running time of computer. After analysis result contrast, Fig. 8 has reflected that the time dependent result of electric-field intensity all unanimously coincide, and increases with the CFL factor, and it is little that Fig. 9 shows the error change of this electric-field intensity.
Claims (3)
1. a Finite Difference-Time Domain separating method of realizing alternating direction implicit with Digital Signal Processing, is characterized in that:
There is electromagnetism computational process twice in the Finite Difference-Time Domain separating method of alternating direction implicit, is expressed as follows respectively
Process one,
(1)
(2)
Process two,
(3)
(4)
Above-mentioned 4 formulas have all met the statement requirement of system performance; Above matrix and vector in various arranged according to the requirement of Digital Signal Processing, then complete the Finite Difference-Time Domain separating method of describing into alternating direction implicit of accompanying drawing 1 to specifications and calculate, can more effectively realize the parallel computation process of many Computer Resources Allocation.
2. a kind of Finite Difference-Time Domain separating method of realizing alternating direction implicit with Digital Signal Processing preforming technique according to claim 1, it is characterized in that: for analog electromagnetic field is in the process of unbounded space, adopt the flexible complete matching layer of coordinate, process the numerical computations that just can complete the flexible complete matching layer of coordinate under this method by recursive convolution further.
3. a kind of Finite Difference-Time Domain separating method of realizing alternating direction implicit with Digital Signal Processing preforming technique according to claim 1, is characterized in that: in the time that 3-D geometric model carries out electromagnetism calculating, in isotropic mediumWithBe three matrix of strips, the representation of this sytem matrix has reflected its characteristics of signals in Fig. 1, is convenient to programming and the corresponding data processing of computer.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107153721A (en) * | 2017-01-03 | 2017-09-12 | 金陵科技学院 | A kind of pungent Fdtd Method Electromagnetic Simulation method under moving target |
| CN108304157A (en) * | 2016-05-24 | 2018-07-20 | 杜玮嘉 | Integrator computing circuit based on memristor |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN108304157A (en) * | 2016-05-24 | 2018-07-20 | 杜玮嘉 | Integrator computing circuit based on memristor |
| CN107153721A (en) * | 2017-01-03 | 2017-09-12 | 金陵科技学院 | A kind of pungent Fdtd Method Electromagnetic Simulation method under moving target |
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Application publication date: 20160518 |