A Bi-CG type iterative method for Drazin-inverse solution of singular inconsistent nonsymmetric linear systems of arbitrary index.
A brief review of some application driven fast algorithms for elliptic partial differential equations
Some application driven fast algorithms developed by the author and his collaborators for elliptic partial differential equations are briefly reviewed here. Subsequent use of the ideas behind development of these algorithms for further development of other algorithms some of which are currently in progress is briefly mentioned. Serial and parallel implementation of these algorithms and their applications to some pure and applied problems are also briefly reviewed.
A Capacitance Matrix Method for Dirichlet Problem on Polygon Region.
A Carleman function and the Cauchy problem for the Laplace equation.
A characterization of balls using the domain derivative.
A combined method for computing the field of the point source in a waveguide. (A weakly curved layered medium).
A combined method for computing the field of the point source in a waveguide (plane-layered media).
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 counterexample to the “hot spots" conjecture.
A counterexample to the -Hodge decomposition
We construct a bounded domain with the cone property and a harmonic function on Ω which belongs to for all 1 ≤ p < 4/3. As a corollary we deduce that there is no -Hodge decomposition in for all p > 4 and that the Dirichlet problem for the Laplace equation cannot be in general solved with the boundary data in for all p > 4.
A direct method for boundary integral equations on a contour with a peak.
A directional compactification of the complex Bloch variety.
A family of finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems
A family of sixth-order compact finite-difference schemes for the three-dimensional Poisson equation.
A few results about the -Laplace's operator.
A finite element method for domain decomposition with non-matching grids
In this note, we propose and analyse a method for handling interfaces between non-matching grids based on an approach suggested by Nitsche (1971) for the approximation of Dirichlet boundary conditions. The exposition is limited to self-adjoint elliptic problems, using Poisson’s equation as a model. A priori and a posteriori error estimates are given. Some numerical results are included.
A finite element method for domain decomposition with non-matching grids
In this note, we propose and analyse a method for handling interfaces between non-matching grids based on an approach suggested by Nitsche (1971) for the approximation of Dirichlet boundary conditions. The exposition is limited to self-adjoint elliptic problems, using Poisson's equation as a model. A priori and a posteriori error estimates are given. Some numerical results are included.
A finite element method for exterior interface problems.
A finite element method on composite grids based on Nitsche’s method
In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.
A finite element method on composite grids based on Nitsche's method
In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.