An Adaptive High Order Direct Solution Technique for Elliptic Boundary Value Problems
An Adaptive High Order Direct Solution Technique for Elliptic Boundary Value Problems
复制标题
椭圆边值问题的自适应高阶直接求解技术
DOI：
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复制
发表时间：
2017
影响因子：
3.1
通讯作者：
A. Gillman
中科院分区：
文献类型：
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作者：
P. Geldermans;A. Gillman
本文提出一种求解椭圆边值问题的自适应高阶离散方法。该技术被应用到一个更新版本的分层庞加莱-Steklov（HPS）方法。粗略地说，HPS方法是基于与Poincare-Steklov算子粘合在一起的局部伪谱离散。新版本采用了一种改进的张量积基，比以前的版本更高效、更稳定。自适应技术利用基函数的张量积性质来创建用于确定需要额外细化的域的部分的标准。由此产生的离散化达到用户规定的精度，并带有一个有效的直接求解器。直接求解器的适用范围增加了时间相关的问题，解决椭圆问题的成本以前限制使用隐式时间步进计划。
This manuscript presents an adaptive high order discretization technique for elliptic boundary value problems. The technique is applied to an update version of the Hierarchical Poincare-Steklov (HPS) method. Roughly speaking, the HPS method is based local pseudospectral discretizations glued together with Poincare-Steklov operators. The new version a modified tensor product basis which is more efficient and stable than previous versions. The adaptive technique exploits the tensor product nature of the basis functions to create a criterion for determining the parts of the domain that require additional refinement. The resulting discretization achieves the user prescribed accuracy and comes with an efficient direct solver. The direct solver increases the range of applicability to time dependent problems where the cost of solving elliptic problems previously limited the use of implicit time stepping schemes.