A spectral collocation method based on Haar wavelets for Poisson equations and biharmonic equations
A spectral collocation method based on Haar wavelets for Poisson equations and biharmonic equations
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DOI：
10.1016/j.mcm.2011.07.006
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发表时间：
2011-12
期刊：
影响因子：
--
通讯作者：
Zhi Shi;Yong Cao
中科院分区：
文献类型：
--
作者：
Zhi Shi;Yong Cao
在这项工作中，我们提出了一种计算方法来解决泊松方程和双调和方程的基础上使用哈尔小波。第一种是将谱系数转换为节点变量值。第二种方法使用克罗内克积来构造水平块和垂直块的张量积网格上的导数近似。最后，求解得到的代数方程组。四个数值算例表明了该方法的有效性。
In this work, we present a computational method for solving Poisson equations and biharmonic equations which are based on the use of Haar wavelets. The first transform the spectral coefficients into the nodal variable values. The second use Kronecker products to construct the approximations for derivatives over a tensor product grid of the horizontal and vertical blocks. Finally, solve the obtained system of algebraic equations. The efficiency of the method is demonstrated by four numerical examples.