A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations
In this paper, the coupled equations in velocity and magnetic field for unsteady magnetohydrodynamic (MHD) flow through a pipe of rectangular section are solved using combined finite volume method and spectral element technique, improved by means of ...
Adaptive sparse grid algorithms with applications to electromagnetic scattering under uncertainty
We discuss adaptive sparse grid algorithms for stochastic differential equations with a particular focus on applications to electromagnetic scattering by structures with holes of uncertain size, location, and quantity. Stochastic collocation (SC) ...
On Numerov's method for a class of strongly nonlinear two-point boundary value problems
The purpose of this paper is to give a numerical treatment for a class of strongly nonlinear two-point boundary value problems. The problems are discretized by fourth-order Numerov's method, and a linear monotone iterative algorithm is presented to ...
Higher order optimization and adaptive numerical solution for optimal control of monodomain equations in cardiac electrophysiology
In this work adaptive and high resolution numerical discretization techniques are demonstrated for solving optimal control of the monodomain equations in cardiac electrophysiology. A monodomain model, which is a well established model for describing the ...
A dimensional split preconditioner for Stokes and linearized Navier-Stokes equations
In this paper we introduce a new preconditioner for linear systems of saddle point type arising from the numerical solution of the Navier-Stokes equations. Our approach is based on a dimensional splitting of the problem along the components of the ...
Iterative adaptive RBF methods for detection of edges in two-dimensional functions
Radial basis functions have gained popularity for many applications including numerical solution of partial differential equations, image processing, and machine learning. For these applications it is useful to have an algorithm which detects edges or ...
Numerical solutions of a two-phase membrane problem
In this paper different numerical methods for a two-phase free boundary problem are discussed. In the first method a novel iterative scheme for the two-phase membrane is considered. We study the regularization method and give an a posteriori error ...
Optimization, resolution and application of composite compact finite difference templates
Spectral-like compact finite differencing schemes are capable of achieving high spatial efficiency of complex physics in irregular domains with difficult boundary conditions. Their low-resolution errors are commonly reached through large stencils sizes ...
Jacobi spectral solution for integral algebraic equations of index-2
This paper is concerned with obtaining the approximate solution of a class of semi-explicit Integral Algebraic Equations (IAEs) of index-2. A Jacobi collocation method including the matrix-vector multiplication representation is proposed for the IAEs of ...