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In this paper we consider second order elliptic partial differential equations with highly varying (heterogeneous) coefficients on a two-dimensional region. The problems are discretized by a composite finite element (FE) and discontinuous Galerkin (DG) Method. The fine grids are in general nonmatching across the subdomain boundaries, and the subdomain partitioning does not need to resolve the jumps in the coefficient. A FETI-DP preconditioner is proposed and analyzed to solve the resulting linear system. Numerical results are presented to support our theory.
Numerical simulation of flow problems and wave propagation in heterogeneous media has important applications in many engineering areas. However, numerical solutions on the fine grid are often prohibitively expensive, and multiscale model reduction te
In this paper we design and analyze a uniform preconditioner for a class of high order Discontinuous Galerkin schemes. The preconditioner is based on a space splitting involving the high order conforming subspace and results from the interpretation o
We deal with the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) preconditioner for elliptic problems discretized by the virtual element method (VEM). We extend the result of [22] to the three dimensional case. We prove polylogarithm
In this work, we propose a local multiscale model reduction approach for the time-domain scalar wave equation in a heterogenous media. A fine mesh is used to capture the heterogeneities of the coefficient field, and the equation is solved globally on
In this paper, we develop a new mass conservative numerical scheme for the simulations of a class of fluid-structure interaction problems. We will use the immersed boundary method to model the fluid-structure interaction, while the fluid flow is gove