Parallel solvers for large eigenvalue problems originating from Maxwell’s equations

1998 ◽  
pp. 771-779 ◽  
Author(s):  
Peter Arbenz ◽  
Roman Geus
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Eigenvalue Problems ◽  
Large Eigenvalue ◽  
Parallel Solvers

FAME

2021 ◽  
Vol 47 (3) ◽  
pp. 1-24
Author(s):  
Xing-long Lyu ◽  
Tiexiang Li ◽  
Tsung-ming Huang ◽  
Jia-wei Lin ◽  
Wen-wei Lin ◽  
...  
Keyword(s):  
Photonic Crystals ◽  
Maxwell’S Equations ◽  
Large Scale ◽  
Maxwell's Equations ◽  
Eigenvalue Problems ◽  
Null Space ◽  
Three Dimensional ◽  
Coefficient Matrix ◽  
Generalized Eigenvalue Problems ◽  
Matrix Vector

In this article, we propose the Fast Algorithms for Maxwell’s Equations (FAME) package for solving Maxwell’s equations for modeling three-dimensional photonic crystals. FAME combines the null-space free method with fast Fourier transform (FFT)-based matrix-vector multiplications to solve the generalized eigenvalue problems (GEPs) arising from Yee’s discretization. The GEPs are transformed into a null-space free standard eigenvalue problem with a Hermitian positive-definite coefficient matrix. The computation times for FFT-based matrix-vector multiplications with matrices of dimension 7 million are only 0.33 and 3.6 × 10 − 3 seconds using MATLAB with an Intel Xeon CPU and CUDA C++ programming with a single NVIDIA Tesla P100 GPU, respectively. Such multiplications significantly reduce the computational costs of the conjugate gradient method for solving linear systems. We successfully use FAME on a single P100 GPU to solve a set of GEPs with matrices of dimension more than 19 million, in 127 to 191 seconds per problem. These results demonstrate the potential of our proposed package to enable large-scale numerical simulations for novel physical discoveries and engineering applications of photonic crystals.

scholarly journals Convergence analysis of a Galerkin boundary element method for electromagnetic resonance problems

2021 ◽  
Vol 2 (3) ◽  
Author(s):  
Gerhard Unger
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Convergence Analysis ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Eigenvalue Problems ◽  
Galerkin Approximation ◽  
Resonance Problem ◽  
Galerkin Boundary Element Method ◽  
Element Method

AbstractIn this paper a convergence analysis of a Galerkin boundary element method for resonance problems arising from the time harmonic Maxwell’s equations is presented. The cavity resonance problem with perfect conducting boundary conditions and the scattering resonance problem for impenetrable and penetrable scatterers are treated. The considered boundary integral formulations of the resonance problems are eigenvalue problems for holomorphic Fredholm operator-valued functions, where the occurring operators satisfy a so-called generalized Gårding’s inequality. The convergence of a conforming Galerkin approximation of this kind of eigenvalue problems is in general only guaranteed if the approximation spaces fulfill special requirements. We use recent abstract results for the convergence of the Galerkin approximation of this kind of eigenvalue problems in order to show that two classical boundary element spaces for Maxwell’s equations, the Raviart–Thomas and the Brezzi–Douglas–Marini boundary element spaces, satisfy these requirements. Numerical examples are presented, which confirm the theoretical results.

A time domain, weighted residual formulation of Maxwell's equations

1993 ◽  
Author(s):  
JEFFREY YOUNG ◽  
FRANK BRUECKNER
Keyword(s):  
Time Domain ◽  
Maxwell’S Equations ◽  
Maxwell's Equations

Sumudu Applications to Maxwell's Equations

PIERS Online ◽  
2009 ◽  
Vol 5 (4) ◽  
pp. 355-360 ◽  
Author(s):  
Fethi Bin Muhammad Belgacem
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations

Maxwell’s Equations versus Newton’s Third Law

2018 ◽  
Author(s):  
Glyn Kennell ◽  
Richard Evitts
Keyword(s):  
Electric Fields ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Simulated Data ◽  
Numerical Data ◽  
Transport Equations ◽  
Concentration Gradients ◽  
Third Law

The presented simulated data compares concentration gradients and electric fields with experimental and numerical data of others. This data is simulated for cases involving liquid junctions and electrolytic transport. The objective of presenting this data is to support a model and theory. This theory demonstrates the incompatibility between conventional electrostatics inherent in Maxwell's equations with conventional transport equations. <br>

The Inverse Source Problem for Maxwell's Equations

2006 ◽  
Author(s):  
Richard A. Albanese ◽  
Peter B. Monk
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Inverse Source Problem

scholarly journals Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations

2021 ◽  
Author(s):  
Jörg Nick ◽  
Balázs Kovács ◽  
Christian Lubich
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Fully Discrete
Sign in / Sign up

Export Citation Format

Share Document