A High-Precision Integration Scheme for the Spectral-Element Time-Domain Method in Electromagnetic Simulation

• Published in: IEEE transactions on antennas and propagation Vol. 57; no. 10; pp. 3223 - 3231
• Main Authors: JIEFU CHEN, LEE, Joon-Ho, QING HUO LIU
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.10.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Antennas; Applied classical electromagnetism; Computational modeling; Differential equations; Discretization; Electromagnetic devices; Electromagnetic fields; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; electron and ion optics; Exact sciences and technology; Finite difference methods; Finite element methods; Fundamental areas of phenomenology (including applications); High-precision integration (HPI) scheme; Mathematical analysis; Matrices; matrix exponential; Matrix methods; Maxwell equations; Maxwell's equations; Physics; Spectra; spectral-element time-domain (SETD) method; Symmetric matrices; Time domain analysis; Time integration; Transient analysis; Spectral method; spectral-element time-domain (SETD) method; Electromagnetism; Numerical integration; matrix exponential; Digital simulation; High precision; High-precision integration (HPI) scheme; Maxwell's equations; Maxwell equations; Time dependence; Algorithms; Time domain method; Discretization
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2009.2028633

A high-precision integration (HPI) scheme combined with the spectral-element time-domain (SETD) method is presented to solve the time-dependent Maxwell's equations. Spatial discretization by spectral elements will lead to block diagonal mass matrices, thus greatly alleviating the computational burden of inverting the mass matrices. A high-precision time integration method based on the matrix exponential is then employed to solve the discretized SETD system. Numerical examples demonstrate that this algorithm is unconditionally stable and very accurate.