Sheng-Jian Lai

Meshless Radial Basis Function Method for Transient Electromagnetic Computations

We propose a novel numerical method to simulate transient electromagnetic problems. The time derivatives are still tackled with the customary explicit leapfrog time scheme. But in the space domain, the fields at the collocation points are expanded into a series of radial basis functions and are treated with a meshless method procedure. Our method solves numerically Maxwells equations with various assigned boundary conditions and current source excitation. Furthermore, the numerical stability condition of our method is obtained through a one-dimensional (1-D) wave equation and thus the relationship between control parameters is accounted for. To verify the accuracy and effectiveness of the new formulation, we compare the results of the proposed method with those of the conventional finite-difference time-domain method through a 1-D case study with different boundary conditions.

Coupling projection domain decomposition method and Kansa's method in electrostatic problems

Abstract This paper present a novel approach for solving electrostatic problems associated with an asymmetrical shielded stripline and shielded coupled-striplines. This novel approach is based on combination of radial basis functions-based meshless unsymmetric collocation method (also, Kansas method) with projection domain decomposition method. Under this new method, we just need to solve a Steklov–Poincare interface equation and the original problem is solved by computing a series of independent subproblems. Two real problems are solved by the proposed approach to demonstrate the accuracy and efficiency.

SOLVING HELMHOLTZ EQUATION BY MESHLESS RADIAL BASIS FUNCTIONS METHOD

In this paper, we propose a brief and general process to compute the eigenvalue of arbitrary waveguides using meshless method based on radial basis functions (MLM-RBF) interpolation. The main idea is that RBF basis functions are used in a point matching method to solve the Helmholtz equation only in Cartesian system. Two kinds of boundary conditions of waveguide problems are also analyzed. To verify the e-ciency and accuracy of the present method, three typical waveguide problems are analyzed. It is found that the results of various waveguides can be accurately determined by MLM-RBF.

Modified Incomplete Cholesky Factorization for Solving Electromagnetic Scattering Problems

In this paper, we study a class of modified incomplete Cholesky factorization preconditioners LLT with two control parameters including dropping rules. Before computing preconditioners, the modified incomplete Cholesky factorization algorithm allows to decide the sparsity of incomplete factorization preconditioners by two fillin control parameters: (1) p, the number of the largest number p of nonzero entries in each row; (2) dropping tolerance. With RCM reordering scheme as a crucial operation for incomplete factorization preconditioners, our numerical results show that both the number of PCOCG and PCG iterations and the total computing time are reduced evidently for appropriate fill-in control parameters. Numerical tests on harmonic analysis for 2D and 3D scattering problems show the efficiency of our method.

Application of the RBF-based meshless method to solve 2-D time domain Maxwell’s equations

Radial basis functions (RBF), as a meshless technique, is widely applied to solve partial differential equations. In this paper, a meshless RBF method is applied to time domain Maxwells equations and calculates a two-dimensional (2-D) cavity case. The main idea is that the fields in the space domain are expanded into a series of radial basis functions and are treated with a meshless method procedure, and the time derivatives are still tackled with the customary difference scheme. The 2-D cavity numerical experiment has been used to validate the propose technique.

Coupling Projection Domain Decomposition Method and Meshless Collocation Method Using Radial Basis Functions in Electromagnetics

This paper presents an efficient meshless approach for solving electrostatic problems. This novel approach is based on combination of radial basis functions-based meshless unsymmetric collocation method with projection domain decomposition method. Under this new method, we just need to solve a Steklov-Poincare interface equation and the original problem is solved by computing a series of independent sub-problems. An electrostatic problem is used as an example to illustrate the application of the proposed approach. Numerical results that demonstrate the accuracy and efficiency of the method are stated.

Compact 2-D Full-Wave Order-Marching Time-Domain Method with a Memory-Redued Technique

This paper describes a memory-reduced (MR) compact two-dimensional (2-D) order-marching time-domain (OMTD) method for full-wave analyses. To reduce memory requirements in the OMTD method, the divergence theorem is introduced to obtain a memoryefficient matrix equation. A lossy microstrip line is presented to validate the accuracy and efficiency of our algorithm.

EIGENVALUE ANALYSIS OF SPHERICAL RESONANT CAVITY USING RADIAL BASIS FUNCTIONS

This paper applies a meshless method based on radial basis function (RBF) collocation to solve three-dimensional scalar Helmholtz equation in rectangular coordinates and analyze the eigenvalues of spherical resonant cavity. The boundary conditions of spherical cavity are deduced. The RBF interpolation method and the collocation procedure are applied to the Helmholtz and boundary condition equations, and their discretization matrix formulations are obtained. The eigenvalues of spherical resonant cavity with natural conformal node distribution are computed by the proposed method. Their results are agreement with the analytic solution.

Simulation of the 2D TMz modes of time-domain Maxwell's equations by RBF-MLM

This paper mainly discusses the simulation of transverse-magnetic modes respect to z (TMz) of time-domain Maxwells equations by meshless method (MLM) based on Radial Basis Functions (RBF). RBF-MLM is applied to solve the transient Maxwell equations which include multiple field components. The main idea is that the fields in the space domain are expanded into a series of radial basis functions and are treated with a meshless method procedure, and the time derivatives are still tackled with the customary difference scheme. The isotropy numerical wave transmits and forms the concentric circle waveform in the simulation area by RBF-MLM. Last, the 2D cavity numerical experiment has been used to validate the propose technique.

Some new strategies for RCM ordering in solving electromagnetic scattering problems

Abstract We describe some ordering strategies for improving the incomplete Cholesky factorization used in the preconditioned conjugate gradient method applied to electromagnetic scattering problems. Some matrix ordering strategies, derived from the greedy partitioning algorithm for multilevel methods, are combined with RCM ordering. These ordering techniques are tested and compared with normal RCM ordering. Some tuning in selecting special nodes as first and last nodes in reverse Cuthill–McKee ordering is shown to apparently improve the quality of incomplete Cholesky factorization preconditioners.