A basic norm equivalence for the theory of multilevel methods.
A Bi-CG type iterative method for Drazin-inverse solution of singular inconsistent nonsymmetric linear systems of arbitrary index.
A block version of BiCGSTAB for linear systems with multiple right-hand sides.
A Bound for thé Optimum Relaxation Factor for the Successive Overrelaxation Method.
A breakdown-free Lanczos type algorithm for solving linear systems.
A Capacitance Matrix Method for Dirichlet Problem on Polygon Region.
A Chebyshev-like semiiteration for inconsistent linear systems.
A Class of Iterative Methods for Solving Saddle Point Problems.
A Class of Norms of Iterative Methods for Solving Systems of Linear Equations.
A comparison of coupled and uncoupled solvers for the cardiac Bidomain model
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
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...
A Conjugate Gradient Method and a Multigrid Algorithm for Morley' s Finite Element Approximation of the Biharmonic Equation.
A convergence analysis of SOR iterative methods for linear systems with weakH-matrices
It is well known that SOR iterative methods are convergent for linear systems, whose coefficient matrices are strictly or irreducibly diagonally dominant matrices and strong H-matrices (whose comparison matrices are nonsingular M-matrices). However, the same can not be true in case of those iterative methods for linear systems with weak H-matrices (whose comparison matrices are singular M-matrices). This paper proposes some necessary and sufficient conditions such that SOR iterative methods are...
A domain decomposition algorithm for elliptic problems in three dimensions.
A domain embedding method for Dirichlet problems in arbitrary space dimension
A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations
We multiply both sides of the complex symmetric linear system by to obtain a new equivalent linear system, then a dual-parameter double-step splitting (DDSS) method is established for solving the new linear system. In addition, we present an upper bound for the spectral radius of iteration matrix of the DDSS method and obtain its quasi-optimal parameter. Theoretical analyses demonstrate that the new method is convergent when some conditions are satisfied. Some tested examples are given to illustrate...
A Fast Iterative Method for Solving Stationary Heat Conduction Problems on Regions Partitioned into Rectangles.
A fast solver for the first biharmonic boundary value problem.
A FETI-DP preconditioner for mortar methods in three dimensions.
A Finite Element - Capacitane Method for Elliptic Problems on Regions Partitioned into Subregions.