A Boundary Element Method for a Two-Dimensional Interface Problem in Electromagnetics.
A boundary element method for Signorini problems in three dimensions.
A boundary multivalued integral “equation” approach to the semipermeability problem
The present paper concerns the problem of the flow through a semipermeable membrane of infinite thickness. The semipermeability boundary conditions are first considered to be monotone; these relations are therefore derived by convex superpotentials being in general nondifferentiable and nonfinite, and lead via a suitable application of the saddlepoint technique to the formulation of a multivalued boundary integral equation. The latter is equivalent to a boundary minimization problem with a small...
A breakdown-free Lanczos type algorithm for solving linear systems.
A brief overview of Fornberg-like methods for conformal mapping of simply and multiply connected regions.
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. C. Clarke's Space Odyssey and Newton's law of gravity
In his famous tetralogy, Space Odyssey, A. C. Clarke called the calculation of a motion of a mass point in the gravitational field of the massive cuboid a classical problem of gravitational mechanics. This article presents a proposal for a solution to this problem in terms of Newton's theory of gravity. First we discuss and generalize Newton's law of gravitation. We then compare the gravitational field created by the cuboid -- monolith, with the gravitational field of the homogeneous sphere. This...
A C1-P2 finite element without nodal basis
A new finite element, which is continuously differentiable, but only piecewise quadratic polynomials on a type of uniform triangulations, is introduced. We construct a local basis which does not involve nodal values nor derivatives. Different from the traditional finite elements, we have to construct a special, averaging operator which is stable and preserves quadratic polynomials. We show the optimal order of approximation of the finite element in interpolation, and in solving the biharmonic...
A calculus of symbols and convolution semigroups on the Heisenberg group
A Capacitance Matrix Method for Dirichlet Problem on Polygon Region.
A case where balancing is harmful.
A C...-Collocation-like Method for Two-Point Boundary Value Problems.
A center of a polytope: An expository review and a parallel implementation.
A central scheme for shallow water flows along channels with irregular geometry
We present a new semi-discrete central scheme for one-dimensional shallow water flows along channels with non-uniform rectangular cross sections and bottom topography. The scheme preserves the positivity of the water height, and it is preserves steady-states of rest (i.e., it is well-balanced). Along with a detailed description of the scheme, numerous numerical examples are presented for unsteady and steady flows. Comparison with exact solutions illustrate the accuracy and robustness of the numerical...
A central scheme for shallow water flows along channels with irregular geometry
We present a new semi-discrete central scheme for one-dimensional shallow water flows along channels with non-uniform rectangular cross sections and bottom topography. The scheme preserves the positivity of the water height, and it is preserves steady-states of rest (i.e., it is well-balanced). Along with a detailed description of the scheme, numerous numerical examples are presented for unsteady and steady flows. Comparison with exact solutions illustrate the accuracy and robustness of the numerical...
A central WENO-TVD scheme for hyperbolic conservation laws.
A certain class of quadratures.
A certain class of quadratures.
A certain class of quadratures with hat function as a weight function.
A certain integral-recurrence equation with discrete-continuous auto-convolution
Laplace transform and some of the author’s previous results about first order differential-recurrence equations with discrete auto-convolution are used to solve a new type of non-linear quadratic integral equation. This paper continues the author’s work from other articles in which are considered and solved new types of algebraic-differential or integral equations.