Solution of capacitance systems using incomplete Cholesky fixed point iteration

✍ Scribed by White, Daniel A.

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 98 KB
• Volume: 15
• Category: Article
• ISSN: 1069-8299
• DOI: 10.1002/(sici)1099-0887(199905)15:5<375::aid-cnm253>3.0.co;2-s

✦ Synopsis

Application of the Galerkin ®nite element method to the electromagnetic vector wave equation yields an implicit system of equations that must be evolved in time. The left-hand matrix has units of capacitance and is analogous to the mass matrix in continuum mechanics. In this letter we point out the interesting fact that for a Cartesian grid the Cholesky decomposition of the capacitance matrix has the same sparsity as the original matrix, i.e. there is no zero-®ll during the course of the Cholesky decomposition. Therefore an iterative method using the incomplete Cholesky decomposition as a preconditioner is quite ecient for nearly orthogonal quadrilateral or hexahedral grids.