相关论文: Multigrid in H(div) on Axisymmetric Domains
A new fully discrete linearized $H^1$-conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic potential formulation. The proposed method yields numerical…
We design and analyze multigrid methods for the saddle point problems resulting from Raviart-Thomas-N\'ed\'elec mixed finite element methods (of order at least 1) for the Darcy system in porous media flow. Uniform convergence of the…
A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…
We solve Poisson's equation using new multigrid algorithms that converge rapidly. The novel feature of the 2D and 3D algorithms are the use of extra diagonal grids in the multigrid hierarchy for a much richer and effective communication…
This paper is to introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary…
We present a fully pseudo-spectral scheme to solve axisymmetric hyperbolic equations of second order. With the Chebyshev polynomials as basis functions, the numerical grid is based on the Lobbato (for two spatial directions) and Radau (for…
The solution of parameter-dependent linear systems, by classical methods, leads to an arithmetic effort that grows exponentially in the number of parameters. This renders the multigrid method, which has a well understood convergence theory,…
It is shown how various ideas that are well established for the solution of Poisson's equation using plane wave and multigrid methods can be combined with wavelet concepts. The combination of wavelet concepts and multigrid techniques turns…
Standard discretization techniques for boundary integral equations, e.g., the Galerkin boundary element method, lead to large densely populated matrices that require fast and efficient compression techniques like the fast multipole method…
Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and…
This work is about a new two-level solver for Helmholtz equations discretized by finite elements. The method is inspired by two-grid methods for finite-difference Helmholtz problems as well as by previous work on two-level…
The multigrid algorithm is a multilevel approach to accelerate the numerical solution of discretized differential equations in physical problems involving long-range interactions. Multiresolution analysis of wavelet theory provides an…
We present a new multigrid solver that is suitable for the Dirac operator in the presence of disordered gauge fields. The key behind the success of the algorithm is an adaptive projection onto the coarse grids that preserves the near null…
We present a robust and efficient multigrid method for single-patch isogeometric discretizations using tensor product B-splines of maximum smoothness. Our method is based on a stable splitting of the spline space into a large subspace of…
We propose a combination of machine learning and flux limiting for property-preserving subgrid scale modeling in the context of flux-limited finite volume methods for the one-dimensional shallow-water equations. The numerical fluxes of a…
We discuss vertex patch smoothers as overlapping domain decomposition methods for fourth order elliptic partial differential equations. We show that they are numerically very efficient and yield high convergence rates. Furthermore, we…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
We present evidence that multigrid (MG) works for wave equations in disordered systems, e.g. in the presence of gauge fields, no matter how strong the disorder. We introduce a "neural computations" point of view into large scale…
Quasipatterns (two-dimensional patterns that are quasiperiodic in any spatial direction) remain one of the outstanding problems of pattern formation. As with problems involving quasiperiodicity, there is a small divisor problem. In this…
Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the…