THE MULTI-GRID METHOD FOR THE DIFFUSION EQUATION WITH STRONGLY DISCONTINUOUS COEFFICIENTS
THE MULTI-GRID METHOD FOR THE DIFFUSION EQUATION WITH STRONGLY DISCONTINUOUS COEFFICIENTS
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DOI：
10.1137/0902035
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发表时间：
1981-01-01
期刊：
影响因子：
--
通讯作者：
PAINTER, JW
中科院分区：
文献类型：
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作者：
ALCOUFFE, RE;BRANDT, A;PAINTER, JW
本文的主题是应用多重网格方法求解有界区域上的\[ - \nabla \cdot（D（x，y）\nabla U（x，y））+ \sigma（x，y）U（x，y）= f（x，y）\]方程，其中D为正，且D，，和在的内边界上不连续.重点是不连续的数量级inD，当特殊的技术必须应用于恢复多重网格方法，以良好的效率。这些技术是基于交叉的连续性。两个基本的方法，其中一个近似的有限差分算子的粗网格是五点运营商（假设有限差分算子的最好的网格是五点之一），其中一个是九点运营商。
The subject of this paper is the application of the multi-grid method to the solution of \[ - \nabla \cdot (D(x,y)\nabla U(x,y)) + \sigma (x,y)U(x,y) = f(x,y) \] in a bounded regionofwhereDis positive andD,, andfare allowed to be discontinuous across internal boundariesof. The emphasis is on discontinuities of orders of magnitude inD, when special techniques must be applied to restore the multi-grid method to good efficiency. These techniques are based on the continuity ofacross. Two basic methods are derived, one in which the approximating finite difference operators on coarser grids are five point operators (assuming the finite difference operator on the finest grid is a five point one) and one in which they are nine point operators.