scholarly journals Fast Direct Solution of Electromagnetic Scattering from Left-Handed Materials Coated Target over Wide Angle

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Guo-hua Wang ◽  
Ying-bao Geng
Keyword(s):  
Electromagnetic Scattering ◽  
Incident Angle ◽  
Linear Equations ◽  
Computation Time ◽  
Wide Angle ◽  
Memory Consumption ◽  
Scattering Problems ◽  
Left Handed ◽  
Computation Process ◽  
Systems Of Linear Equations

When solving the electromagnetic scattering problems over wide angle, the traditional method of moments (MoM) needs to repeat the solving process of dense systems of linear equations using the iteration method at each incident angle, which proved to be quite inefficient. To circumvent this problem, a fast numerical method based on block LDLT factorization accelerated by adaptive cross approximation (ACA) algorithm is presented to analyze the electromagnetic scattering of left-handed materials (LHM) coated target. The ACA algorithm is applied to impedance matrix filling and all steps of block LDLT factorization process, which can accelerate the computation process and reduce the memory consumption. The numerical results proved that the proposed method is efficient in calculating monostatic RCS of LHM coated target with many required sampling angles. Compared with the traditional MoM, computation time and memory consumption are reduced effectively.

scholarly journals Numerical Simulation of Multiphase Multicomponent Flow in Porous Media: Efficiency Analysis of Newton-Based Method

Fluids ◽  
2021 ◽  
Vol 6 (10) ◽  
pp. 355
Author(s):  
Timur Imankulov ◽  
Danil Lebedev ◽  
Bazargul Matkerim ◽  
Beimbet Daribayev ◽  
Nurislam Kassymbek
Keyword(s):  
Porous Media ◽  
Linear Equations ◽  
Computation Time ◽  
Flow In Porous Media ◽  
Multicomponent Flow ◽  
Original Matrix ◽  
Sparsity Pattern ◽  
Speed Up ◽  
Systems Of Linear Equations ◽  
The One

Newton’s method has been widely used in simulation multiphase, multicomponent flow in porous media. In addition, to solve systems of linear equations in such problems, the generalized minimal residual method (GMRES) is often used. This paper analyzed the one-dimensional problem of multicomponent fluid flow in a porous medium and solved the system of the algebraic equation with the Newton-GMRES method. We calculated the linear equations with the GMRES, the GMRES with restarts after every m steps—GMRES (m) and preconditioned with Incomplete Lower-Upper factorization, where the factors L and U have the same sparsity pattern as the original matrix—the ILU(0)-GMRES algorithms, respectively, and compared the computation time and convergence. In the course of the research, the influence of the preconditioner and restarts of the GMRES (m) algorithm on the computation time was revealed; in particular, they were able to speed up the program.

scholarly journals Application of Two-Dimensional Compressive Sensing to Wavelet Method of Moments for Fast Analysis of Wide-Angle Electromagnetic Scattering Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yi Liu ◽  
Qi Qi ◽  
Xinyuan Cao ◽  
Mingsheng Chen ◽  
Guoqing Deng ◽  
...  
Keyword(s):  
Compressive Sensing ◽  
Method Of Moments ◽  
Electromagnetic Scattering ◽  
Wide Angle ◽  
Two Dimensional ◽  
Induced Current ◽  
Linear Superposition ◽  
Scattering Problems ◽  
Wavelet Method ◽  
Right Hand

To efficiently solve the electromagnetic scattering problems over a wide incident angle, a novel scheme by introducing the two-dimensional compressive sensing theory into the wavelet method of moments is proposed. In this scheme, a linear system of equations with multiple right-hand sides in wavelet domain is formed firstly, and one side of the bilateral sparse transform to the induced current matrix is simultaneously accomplished and then the bilateral measurement of the induced current matrix is operated by the linear superposition of the right-hand side vectors a few times and the extraction of rows from the impedance matrix. Finally, after completing the other side of the bilateral sparse transform, the wide-angle problems can be solved rapidly by two times of recovery algorithm with prior knowledge. The basic principle is elaborated in detail, and the effectiveness is demonstrated by numerical experiments.

Hybrid Accelerated Method via Volume-Surface Integral Equation for Efficient Calculation of Monostatic RCS

2015 ◽  
Vol 719-720 ◽  
pp. 881-885
Author(s):  
Jia Qi Chen ◽  
Yue Yuan Zhang
Keyword(s):  
Electromagnetic Scattering ◽  
Linear Equations ◽  
Iterative Solution ◽  
Low Rank ◽  
Computational Time ◽  
Surface Integral ◽  
Scattering Problems ◽  
Fast Analysis ◽  
Efficient Calculation ◽  
Successive Over Relaxation

A novel efficient hybrid accelerated method is proposed for the fast analysis of the monostatic electromagnetic scattering problems arising from volume-surface integral equations (VSIE) formulation. In the first step, by utilizing the low rank property, several largest eigenvalues and corresponding eigenvectors of the multiple right hand sides can be computed and saved efficiently by adaptive cross approximation (ACA) algorithm. The iterative solution of linear equations is required at these principle eigenvectors. Compared with solving linear equations at each angle repeatedly, the proposed method is able to greatly reduce the number of equations. In the second step, a disturbed symmetric successive over-relaxation (D-SSOR) preconditioner is constructed to speed up the convergence rate of iterative methods. Numerical results demonstrate that the present method can reduce the computational time significantly for monostatic VSIE calculation with high accuracy.

GPS Navigation Solutions by Analogue Neural Network Least-Squares Processors

2005 ◽  
Vol 58 (1) ◽  
pp. 105-118 ◽  
Author(s):  
Dah-Jing Jwo
Keyword(s):  
Least Squares ◽  
Digital Computer ◽  
Linear Equations ◽  
Computation Time ◽  
Gps Navigation ◽  
Systems Of Linear Equations ◽  
Single Epoch ◽  
Pseudo Inverse ◽  
Gradient Approach ◽  
Matrix Calculation

The solution for the receiver's position and clock bias using four or more GPS pseudorange measurements involve nonlinear quadratic equations. One of the popular techniques attempts to linearise the equations and solve them by the least-squares (LS) scheme based on an iterative gradient approach. For real-time applications when the solution is to be obtained within a time of the order of a hundred nanoseconds, a digital computer often cannot comply with the desired computation time, or its use is too expensive. In this paper, two ordinary differential equation formulation schemes and corresponding circuits of neuron-like analog processors will be employed for GPS navigation processing. The circuits of simple neuron-like analog processors are employed essentially for solving systems of linear equations based on the criterion of mean square error minimization, which is commonly utilized for determining positioning solutions in the GPS receivers. Experiments on single epoch and thereafter dynamic positioning will be conducted by computer simulation to validate the usefulness of the proposed scheme. The solutions will be assessed and compared to those provided by the conventional method in which pseudo-inverse matrix calculation by digital computer is involved.

scholarly journals A Hybrid 3DMLUV-FIA Method for Scattering from a 3D Dielectric Object above a 2D Dielectric Rough Surface

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Wu Xuezhi ◽  
Wenping Yu
Keyword(s):  
Rough Surface ◽  
Method Of Moments ◽  
Electromagnetic Scattering ◽  
Three Dimensional ◽  
Memory Consumption ◽  
Scattering Problems ◽  
The Matrix ◽  
Speed Up ◽  
Stability And Accuracy ◽  
Time Overhead

The electromagnetic scattering from the composite model of a three-dimensional (3D) dielectric object located above a two-dimensional (2D) dielectric rough surface is analyzed in this work. Poggio, Miller, Chang, Harrington, Wu, and Tsai (PMCHWT) integral equations are discretized by the method of moments (MoM) into a matrix which is solved by Biconjugate Gradients Stabilized (BICGSTAB) method. Method of 3DMLUV was used for PEC object located above rough surface. Comparing to the case when object and rough surface are both PEC, the memory requirement and computational complexity for dielectric models are increased due to doubled unknown number. Moreover, compared to dielectric object in free space, the coupling between dielectric object and dielectric rough surface will result in complicated numerical simulation. To solve this problem, the updated rank based 3D Multilevel UV (3DMLUV) method is employed to reduce memory consumption and CPU time overhead. The 3DMLUV has been successfully applied in the scattering of PEC targets; however, when the object or rough surface becomes dielectric, the coupling between dielectric object and dielectric rough surface will lead to slow constriction. Therefore, the Fast Iterative Approach (FIA) is applied to further speed up the constricted speed of the matrix required in 3DMLUV. The efficiency, stability, and accuracy of the proposed method are demonstrated in a variety of scattering problems.

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