Grid algebra in finite difference methods

Michael P. Lamoureux and Heather K. Hardeman

ABSTRACT

Large, sparse matrices often appear in numerical methods for solving partial differential equations, particularly in finite difference solutions to the wave equation in two and three dimensions. We demonstrate a technique to represent these operators directly on a grid and develop linear algebraic methods to simplify or factor the operator into a form that is easy to solve using back-substitution. We apply the technique to implement an implicit solver for a finite difference algorithm applied to the wave equation in two dimensions.

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