Solving Large Complex Linear Systems with Direct and Iterative Methods in ANSYS

gene.poole@ansys.com

ANSYS Minneapolis

Riverview Office Tower

8009 34^{th}
Avenue S., Site 1475

Bloomington, MN 55425

mheroux@cs.sandia.gov

Sandia National Laboratories

Albuquerque, NM

Abstract

This paper describes the solution of large complex (frequency domain) linear systems in the industrial finite element code ANSYS. The demand for these large complex systems comes from time-harmonic simulation requirements. Typical applications include high-frequency electromagnetic simulation for waveguides or transmission lines, low-frequency electromagnetic simulation for rotating electric machines, acoustics and acoustic-structural interaction, as well as piezoelectric-driven transducers and oscillators. Linear systems with at least several hundred thousand equations are common but future demands are for several million equations and up. A direct sparse solver for complex systems is used effectively to solve large systems up to a few million equations. Basic iterative solvers are also available in ANSYS to solve complex systems.

This paper compares and contrasts the existing approaches and also describes some new collaborative work with an equivalent real formulation (ERF) for solving large complex systems using Komplex, a solver package developed at Sandia National Laboratories. Although ERFs are typically not as efficient as true complex equivalents, formulating the complex problem as an ERF provides access to sophisticated real valued solvers for which there are no complex valued equivalent. Examples are given from industrial problems solved using ANSYS.