Chapter 6

Finite Difference Method

Abstract

This case study discusses how a finite-difference code using a large one-dimensional stencil is optimized on a three-dimensional mesh. Achieving good performance requires maximizing data reuse through use of shared memory. Attention is paid to coalescing global memory accesses for derivatives in all directions and using constant memory effectively.

Keywords

Constant memory; Coalescing; Nonuniform mesh; 1D stencil; Instruction-level parallelism

In many fields of science and engineering, the governing system of equations takes the form of either ordinary or partial differential equations. One method of solving these equations is to use finite differences, where the continuous analytical derivatives are approximated ...

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