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A Fast Direct Solver for a Class of 3-D Elliptic Partial Differential Equation with Variable Coefficient
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- Journal:
- Communications in Computational Physics / Volume 12 / Issue 4 / October 2012
- Published online by Cambridge University Press:
- 20 August 2015, pp. 1148-1162
- Print publication:
- October 2012
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- Article
- Export citation
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We propose a direct solver for the three-dimensional Poisson equation with a variable coefficient, and an algorithm to directly solve the associated sparse linear systems that exploits the sparsity pattern of the coefficient matrix. Introducing some appropriate finite difference operators, we derive a second-order scheme for the solver, and then two suitable high-order compact schemes are also discussed. For a cube containing N nodes, the solver requires
arithmetic operations and 
memory to store the necessary information. Its efficiency is illustrated with examples, and the numerical results are analysed.
arithmetic operations and 
memory to store the necessary information. Its efficiency is illustrated with examples, and the numerical results are analysed.