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A Second Order Accurate Finite Difference Scheme for the Heat Equation on Irregular Domains and Adaptive Grids
Published online by Cambridge University Press: 01 February 2011
Abstract
We present a finite difference scheme for solving the variable coefficient heat equations with Dirichlet boundary conditions on irregular domains. A quadtree data structure is used to represent the non-graded adaptive Cartesian grids, and the interface is represented by the zero value points of the level set function. Numerical results in two spatial dimensions demonstrate second order accuracy for both the solution and its gradient.
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- Copyright © Materials Research Society 2006
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