A numerical scheme for the two phase Mullins-Sekerka problem.
A numerical solution of a two-dimensional transport equation
In this paper we present a variational method for approximating solutions of the Dirichlet problem for the neutron transport equation in the stationary case. Error estimates from numerical examples are used to evaluate an approximation of the solution with respect to the steps of two grids.
A numerical solution of diffraction problems for the radiation transport equation.
A numerical solution of the Dirichlet problem on some special doubly connected regions
The aim of this paper is to give a convergence proof of a numerical method for the Dirichlet problem on doubly connected plane regions using the method of reflection across the exterior boundary curve (which is analytic) combined with integral equations extended over the interior boundary curve (which may be irregular with infinitely many angular points).
A numerical solution using an adaptively preconditioned Lanczos method for a class of linear systems related with the fractional Poisson equation.
A numerical study of effects of the axial stress on unsteady liquid pipeline flows.
A numerical study of eigenvalues of the hyperbolic Laplacian for polyhedra with one cusp.
A Numerical study of Newton interpolation with extremely high degrees
In current textbooks the use of Chebyshev nodes with Newton interpolation is advocated as the most efficient numerical interpolation method in terms of approximation accuracy and computational effort. However, we show numerically that the approximation quality obtained by Newton interpolation with Fast Leja (FL) points is competitive to the use of Chebyshev nodes, even for extremely high degree interpolation. This is an experimental account of the analytic result that the limit distribution of FL...
A numerical study of non-cavitating and cavitating liquid flow around a hydrofoil
The results of a workshop concerning the numerical simulation of the liquid flow around a hydrofoil in non-cavitating and cavitating conditions are presented. This workshop was part of the conference “Mathematical and Numerical aspects of Low Mach Number Flows” (2004) and was aimed to investigate the capabilities of different compressible flow solvers for the low Mach number regime and for flows in which incompressible and supersonic regions are simultaneously present. Different physical models...
A numerical study of non-cavitating and cavitating liquid flow around a hydrofoil
The results of a workshop concerning the numerical simulation of the liquid flow around a hydrofoil in non-cavitating and cavitating conditions are presented. This workshop was part of the conference “Mathematical and Numerical aspects of Low Mach Number Flows” (2004) and was aimed to investigate the capabilities of different compressible flow solvers for the low Mach number regime and for flows in which incompressible and supersonic regions are simultaneously present. Different physical models...
A numerical study of some questions in vortex rings theory
A numerical study on Neumann-Neumann methods for hp approximations on geometrically refined boundary layer meshes II. Three-dimensional problems
In this paper, we present extensive numerical tests showing the performance and robustness of a Balancing Neumann-Neumann method for the solution of algebraic linear systems arising from hp finite element approximations of scalar elliptic problems on geometrically refined boundary layer meshes in three dimensions. The numerical results are in good agreement with the theoretical bound for the condition number of the preconditioned operator derived in [Toselli and Vasseur, IMA J. Numer. Anal.24 (2004)...
A numerically stable least squares solution to the quadratic programming problem
The strictly convex quadratic programming problem is transformed to the least distance problem - finding the solution of minimum norm to the system of linear inequalities. This problem is equivalent to the linear least squares problem on the positive orthant. It is solved using orthogonal transformations, which are memorized as products. Like in the revised simplex method, an auxiliary matrix is used for computations. Compared to the modified-simplex type methods, the presented dual algorithm QPLS...
A Nyström method for boundary integral equations in domains with corners.
A one parameter method for the matrix inverse square root
This paper is motivated by the paper [3], where an iterative method for the computation of a matrix inverse square root was considered. We suggest a generalization of the method in [3]. We give some sufficient conditions for the convergence of this method, and its numerical stabillity property is investigated. Numerical examples showing that sometimes our generalization converges faster than the methods in [3] are presented.
A parallel algorithm for computing the group inverse via Perron complementation.
A parallel algorithm for discrete least squares rational approximation.
A parallel algorithm for solving band systems and matrix inversion
A parallel algorithm for the eigenvalues and eigenvectors of a general complex matrix.
A parallel algorithm for two phase multicomponent contaminant transport
We discuss the formulation of a simulator in three spatial dimensions for a multicomponent, two phase (air, water) system of groundwater flow and transport with biodegradation kinetics and wells with multiple screens. The simulator has been developed for parallel, distributed memory, message passing machines. The numerical procedures employed are a fully implicit expanded mixed finite element method for flow and either a characteristics-mixed method or a Godunov method for transport and reactions...