Related papers: Multigrid as an exact solver
The set of common numerical and analytical problems is introduced in the form of the generalized multidimensional discrete Poisson equation. It is shown that its solutions with square-summable discrete derivatives are unique up to a…
In this work, we propose a robust and easily implemented algebraic multigrid method as a stand-alone solver or a preconditioner in Krylov subspace methods for solving either symmetric and positive definite or saddle point linear systems of…
Numerical methods for the transmission eigenvalue problems are hot topics in recent years. Based on the work of Lin and Xie [Math. Comp., 84(2015), pp. 71-88], we build a multigrid method to solve the problems. With our method, we only need…
The multigrid methodology is reviewed. By integrating numerical processes at all scales of a problem, it seeks to perform various computational tasks at a cost that rises as slowly as possible as a function of $n$, the number of degrees of…
We present a multigrid algorithm for self consistent solution of the Kohn-Sham equations in real space. The entire problem is discretized on a real space mesh with a high order finite difference representation. The resulting self consistent…
The solution of saddle-point problems, such as the Stokes equations, is a challenging task, especially in large-scale problems. Multigrid methods are one of the most efficient solvers for such systems of equations and can achieve…
The convergence of multigrid methods degrades significantly if a small number of low quality cells are present in a finite element mesh, and this can be a barrier to the efficient and robust application of multigrid on complicated geometric…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
This paper introduces a weighted generalized inverse framework for Fourier extensions, designed to suppress spurious oscillations in the extended region while maintaining high approximation accuracy on the original interval. By formulating…
We propose a hybrid iterative method based on MIONet for PDEs, which combines the traditional numerical iterative solver and the recent powerful machine learning method of neural operator, and further systematically analyze its theoretical…
With the hardware support for half-precision arithmetic on NVIDIA V100 GPUs, high-performance computing applications can benefit from lower precision at appropriate spots to speed up the overall execution time. In this paper, we investigate…
In this paper we obtain new sufficient conditions for representation of a function as an absolutely convergent Fourier integral. Unlike those known earlier, these conditions are given in terms of belonging to weighted spaces. Adding weights…
In some cases, computational benefit can be gained by exploring the hyper parameter space using a deterministic set of grid points instead of a Markov chain. We view this as a numerical integration problem and make three unique…
Many problems in beam physics and plasma physics require the solution of Poisson's equation with free-space boundary conditions. The algorithm proposed by Hockney and Eastwood is a popular scheme to solve this problem numerically, used by…
In many practical applications of numerical methods a substantial increase in efficiency can be obtained by using local grid refinement, since the solution is generally smooth in large parts of the domain and large gradients occur only…
Smoothing properties of two-color distributive relaxation for solving a two-dimensional (2D) Stokes flow by multigrid method are theoretically investigated by using the local Fourier analysis (LFA) method. The governing equation of the 2D…
We discuss the ill conditioning of the matrix for the discretised Poisson equation in the small aspect ratio limit, and motivate this problem in the context of nonhydrostatic ocean modelling. Efficient iterative solvers for the Poisson…
In potential theory, use of barriers is one of the most important techniques. We construct strong barriers for weighted quasilinear elliptic operators. There are two applications: (i) solvability of Poisson-type equations with boundary…
This manuscript presents a fast direct solution technique for solving two dimensional wave scattering problems from quasi-periodic multilayered structures. When the interface geometries are complex, the dominant term in the computational…
Although the linear method is one of the most robust algorithms for optimizing non-linearly parametrized wavefunctions in variational Monte Carlo, it suffers from a memory bottleneck due to the fact at each optimization step a generalized…