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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

Han Chen ,
Chohong Min  and
Frederic Gibou
Han Chen
Affiliation:
Department of Computer Science, Univesity of California, Santa Barbara, CA, 93106
Chohong Min
Affiliation:
chohong@math.ucsb.edu, University of California, Department of Mathematics, Santa Barbara, CA, 93106, United States
Frederic Gibou
Affiliation:
fgibou@engineering.ucsb.edu, University of California, Department of Mechanical Engineering & Department of Computer Science, Santa Barbara, CA, 93106, United States
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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.

Keywords

simulationcrystal growthmolecular beam epitaxy (MBE)
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 910: Symposium A – Amorphous and Polycrystalline Thin-Film Silicon Science and Technology – 2006 , 2006 , 0910-A05-07
Copyright
Copyright © Materials Research Society 2006

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References

1. Chen, H., Min, C., and Gibou, F. A supra-convergent finite difference scheme for the Poisson and heat equations on irregular domains and non-graded adaptive grids. (under review)Google Scholar
2. Juric, D., and Tryggvason, G. A front tracking method for dendritic solidification. J. Comput. Phys. 123, 127, 1996.Google Scholar
3. Karma, A., and Rappel, W. Quantitative phase-field modeling of dendritic growth in two and three dimensions. Phys. Rev. E., 57, 4323, 1997.Google Scholar
4. Osher, S., and Sethian, J. Front propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulation. J. Comput. Phys., 79, 12, 1988.Google Scholar