High Order Finite Difference Discretization for Composite Grid Hierarchy and Its Applications (Communications in Computational Physics, 2020)
We introduce efficient approaches to construct high order finite differencediscretizations for solving partial differential equations, based on a composite gridhierarchy. We introduce a modification of the traditional point clustering algorithm,obtained by adding restrictive parameters that control the minimal patch length andthe size of the buffer zone. As a result, a reduction in the number of interfacial cells isobserved. Based on a reasonable geometric grid setting, we discuss a general approachfor the construction of stencils in a composite grid environment. The straightforwardapproach leads to an ill-posed problem. In our approach we regularize this problem,and transform it into solving a symmetric system of linear of equations. Finally, astencil repository has been designed to further reduce computational overhead. Theeffectiveness of the discretizations is illustrated by numerical experiments on secondorder elliptic differential equations.