Related papers: Analysis of hierarchical SSOR for three dimensiona…
We propose V--cycle multigrid methods for vector field problems arising from the lowest order hexahedral N\'{e}d\'{e}lec finite element. Since the conventional scalar smoothing techniques do not work well for the problems, a new type of…
We propose a systemic method of applying the auxiliary systems of original equations to find the high order nonlocal symmetries of nonlinear evolution equation. In order to validate the effectiveness of the method, some examples are…
The choice of relaxation parameter in the projected successive overrelaxation (PSOR) method for nonnegative quadratic programming problems is problem-dependent. We present novel adaptive PSOR algorithms that adaptively control the…
The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…
This work introduces a new higher-order accurate super compact (HOSC) finite difference scheme for solving complex unsteady three-dimensional (3D) non-Newtonian fluid flow problems. As per the author's knowledge, the proposed scheme is the…
We compute the structure of a self-gravitating torus with polytropic equation-of-state (EOS) rotating in an imposed centrifugal potential. The Poisson-solver is based on isotropic multigrid with optimal covering factor (fluid…
In the tensor completion problem, one seeks to estimate a low-rank tensor based on a random sample of revealed entries. In terms of the required sample size, earlier work revealed a large gap between estimation with unbounded computational…
The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…
The estimation of correspondences between two images resp. point sets is a core problem in computer vision. One way to formulate the problem is graph matching leading to the quadratic assignment problem which is NP-hard. Several so called…
In this paper, we present the Stroboscopic Averaging Method (SAM), recently introduced in [7,8,10,12], which aims at numerically solving highly-oscillatory differential equations. More specifically, we first apply SAM to the Schr\"odinger…
This paper concerns the structural stability of smooth cylindrically symmetric supersonic Euler-Poisson flows in nozzles. Both three-dimensional and axisymmetric perturbations are considered. On one hand, we establish the existence and…
High-performance Ising machines for solving combinatorial optimization problems have been developed with digital processors implementing heuristic algorithms such as simulated bifurcation (SB). Although Ising machines have been designed for…
We consider accelerated versions of the operator Sinkhorn iteration (OSI) for solving scaling problems for completely positive maps. Based on the interpretation of OSI as alternating fixed point iteration, it has been recently proposed to…
Because the expense of estimating the optimal value of the relaxation parameter in the successive over-relaxation (SOR) method is usually prohibitive, the parameter is often adaptively controlled. In this paper, new adaptive SOR methods are…
Over the years, Isogeometric Analysis has shown to be a successful alternative to the Finite Element Method (FEM). However, solving the resulting linear systems of equations efficiently remains a challenging task. In this paper, we consider…
We devise a Hybrid High-Order (HHO) method for highly oscillatory elliptic problems that is capable of handling general meshes. The method hinges on discrete unknowns that are polynomials attached to the faces and cells of a coarse mesh;…
While multilinear algebra appears natural for studying the multiway interactions modeled by hypergraphs, tensor methods for general hypergraphs have been stymied by theoretical and practical barriers. A recently proposed adjacency tensor is…
This article concerns the global-in-time existence of smooth solutions with small amplitude to two space dimensional Euler-Poisson system. The main difficulty lies in the slow time decay $(1+t)^{-1}$ of the linear system. Inspired by Ozawa,…
This paper presents a matrix-free multigrid method for solving the Stokes problem, discretized using $H^{\text{div}}$-conforming discontinuous Galerkin methods. We employ a Schur complement method combined with the fast diagonalization…
A general local Fourier analysis for overlapping block smoothers on triangular grids is presented. This analysis is explained in a general form for its application to problems with different discretizations. This tool is demonstrated for…