This dissertation presents an efficient and high-order boundary integral solver for the Stokes equations in complex 3D geometries. The targeted applications of this solver are the flow problems in domains involving moving boundaries. In such problems, traditional finite element methods involving 3D unstructured mesh generation experience difficulties. Our solver uses the indirect boundary integ...

Fourth-order boundary value problems are solved by means of exponentially-fitted methods of different orders. These methods, which depend on a parameter, can be constructed following a six-step flow chart of Ixaru and Vanden Berghe. Special attention is paid to the expression of the error term and to the choice of the parameter in order to make the error as small as possible. Some numerical exa...

A new approach based on the finite-difference technique has been developed to study the steady incompressible Navier-Stokes equations in the laminar region, where the domain is partially bounded by a free surface. The nonstaggered fractional step method is used to solve the flow equations written in terms of primitive variables. The physical domain is transformed to a rectangle by means of a nu...

The medial axis (MA) of an object is homotopy equivalent to the solid model. This makes the medial axis a natural candidate for a skeleton representation of a general solid object. In addition, the medial axis transform (MAT) is useful for many applications in computer graphics and other areas. In many applications it is not only important to have a description of the skeleton, but also to have...

Let P d n be the the space of real algebraic polynomials of d variables and degree at most n, K ⊂ R a compact set, ||p||K := supx∈K |p(x)| the usual supremum norm on K, card(Y ) the cardinality of a finite set Y . A family of sets Y = {Yn ⊂ K, n ∈ N} is called an admissible mesh in K if there exists a constant c1 > 0 depending only on K such that ||p||K ≤ c1||p||Yn , p ∈ P d n , n ∈ N, where th...

In this paper we present a new algorithm to create fair discrete surfaces satisfying prescribed G1 boundary constraints. All surfaces are built by discretizing a partial differential equation based on pure geometric intrinsics. The construction scheme is designed to produce meshes that are partitioned into regular domains. Using this knowledge in advance we can develop a fast iterative algorith...

we present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. numerical method of sixth-order with end conditions of the order 6 is derived. the convergence analysis of the method has been discussed. numerical examples are presented to illustra...

This paper deals with numerical solution of singularly perturbed delay parabolic reaction diffusion problem having large on the spatial variable non-local boundary condition. The exhibits layer both sides domain and interior is also created. Introducing a fitting parameter into asymptotic applying average finite difference approximation, fitted operator method developed for solving under consid...