标题： 多网格高阶网格细化技术 显示英文标题

标题： Multigrid High Order Mesh Refinement Techniques

摘要： 一种用于执行高阶网格细化多重网格计算的方法被提出。 利用全近似方案（FAS）多重网格技术对一系列分辨率逐渐增加的嵌套补丁进行处理。 通过额外的缺陷校正项在粗尺度上生成守恒形式，以抵消边界处的局部过量通量。 给出了任意阶数的公式，扩展了Bai和Brandt现有的技术。 针对三维中的奇点源进行了测试计算，这些计算展示了多重网格的收敛特性、数值精度以及方法的正确阶数。 讨论了所有电子量子化学计算的应用。 显示英文摘要

摘要： A method for performing high order mesh refinement multigrid computations is presented. The Full Approximation Scheme (FAS) multigrid technique is utilized for a sequence of nested patches of increasing resolution. Conservation forms are generated on coarse scales by additional defect correction terms which counter the local excess fluxes at the boundaries. Formulas are given for arbitrary order, extending the existing technique of Bai and Brandt. Test calculations are presented for a singular source in three dimensions which illustrate the multigrid convergence properties, numerical accuracy, and correct order of the approach. Applications for all electron quantum chemical computations are discussed.