Related papers: High order two-grid finite difference methods for …
In this paper, a symmetrized two-scale finite element method is proposed for a class of partial differential equations with symmetric solutions. With this method, the finite element approximation on a fine tensor product grid is reduced to…
The aim of this paper is to design an efficient multigrid method for constrained convex optimization problems arising from discretization of some underlying infinite dimensional problems. Due to problem dependency of this approach, we only…
We present a new meshless method for scalar diffusion equations which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of…
In this paper, we propose a mesh-free method to solve interface problems using the deep learning approach. Two interface problems are considered. The first one is an elliptic PDE with a discontinuous and high-contrast coefficient. While the…
In this paper, a direct finite element method is proposed for solving interface problems on unfitted meshes. This new method treats the two interface conditions as an $H^{\frac12}(\Gamma)\times H^{-\frac12}(\Gamma)$ pair for the mutual…
Internal interfaces in a domain could exist as a material defect or they can appear due to propagations of cracks. Discretization of such geometries and solution of the contact problem on the internal interfaces can be computationally…
The automated finite element analysis of complex CAD models using boundary-fitted meshes is rife with difficulties. Immersed finite element methods are intrinsically more robust but usually less accurate. In this work, we introduce an…
A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular interfaces. Since the solution has low regularity across…
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…
Elastic materials are ubiquitous in nature and indispensable components in man-made devices and equipments. When a device or equipment involves composite or multiple elastic materials, elasticity interface problems come into play. The…
Efforts to achieve better accuracy in numerical relativity have so far focused either on implementing second order accurate adaptive mesh refinement or on defining higher order accurate differences and update schemes. Here, we argue for the…
Adaptive interface-Mesh un-Refinement (AiMuR) based Sharp-Interface Level-Set-Method (SI-LSM) is proposed for both uniform and non-uniform Cartesian-Grid. The AiMuR involves interface location based dynamic un-refinement (with merging of…
This paper proposes a Cartesian grid-based boundary integral method for efficiently and stably solving two representative moving interface problems, the Hele-Shaw flow and the Stefan problem. Elliptic and parabolic partial differential…
Stokes flow equations have been implemented successfully in practice for simulating problems with moving interfaces. Though computational methods produce accurate solutions and numerical convergence can be demonstrated using a resolution…
Context: Calculating stellar pulsations requires a sufficient accuracy to match the quality of the observations. Many current pulsation codes apply a second order finite-difference scheme, combined with Richardson extrapolation to reach…
We develop a fourth order accurate finite difference method for the three dimensional elastic wave equation in isotropic media with the piecewise smooth material property. In our model, the material property can be discontinuous at curved…
When using a finite difference method to solve an initial--boundary--value problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze…
This paper develops and analyses numerical approximation for linear-quadratic optimal control problem governed by elliptic interface equations. We adopt variational discretization concept to discretize optimal control problem, and apply an…
In the past decades, the finite difference methods for space fractional operators develop rapidly; to the best of our knowledge, all the existing finite difference schemes, including the first and high order ones, just work on uniform…
The matched interface and boundary (MIB) method has a proven ability for delivering the second order accuracy in handling elliptic interface problems with arbitrarily complex interface geometries. However, its collocation formulation…