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2-dimensional primal domain decomposition theory in detail

Dalibor Lukáš, Jiří Bouchala, Petr Vodstrčil, Lukáš Malý (2015)

Applications of Mathematics

We give details of the theory of primal domain decomposition (DD) methods for a 2-dimensional second order elliptic equation with homogeneous Dirichlet boundary conditions and jumping coefficients. The problem is discretized by the finite element method. The computational domain is decomposed into triangular subdomains that align with the coefficients jumps. We prove that the condition number of the vertex-based DD preconditioner is O ( ( 1 + log ( H / h ) ) 2 ) , independently of the coefficient jumps, where H and h denote...

A comparison of coupled and uncoupled solvers for the cardiac Bidomain model

P. Colli Franzone, L. F. Pavarino, S. Scacchi (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The aim of this work is to compare a new uncoupled solver for the cardiac Bidomain model with a usual coupled solver. The Bidomain model describes the bioelectric activity of the cardiac tissue and consists of a system of a non-linear parabolic reaction-diffusion partial differential equation (PDE) and an elliptic linear PDE. This system models at macroscopic level the evolution of the transmembrane and extracellular electric potentials of the anisotropic cardiac tissue. The evolution equation is...

A comparison of the accuracy of the finite-difference solution to boundary value problems for the Helmholtz equation obtained by direct and iterative methods

Václav Červ, Karel Segeth (1982)

Aplikace matematiky

The development of iterative methods for solving linear algebraic equations has brought the question of when the employment of these methods is more advantageous than the use of the direct ones. In the paper, a comparison of the direct and iterative methods is attempted. The methods are applied to solving a certain class of boundary-value problems for elliptic partial differential equations which are used for the numerical modeling of electromagnetic fields in geophysics. The numerical experiments...

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