An isogeometric boundary element method is applied to simulate wave scattering problems governed by the Helmholtz equation. The NURBS (non-uniform rational B-splines) widely used in CAD (computer aided design) field represent geometric model and approximate physical variables. Burton-Miller formulation overcome fictitious frequency problem when using a single integral equation for exterior boun...

NURBS surfaces can be non-uniform and defined for any degree, but existing subdivision surfaces are either uniform or of fixed degree. The resulting incompatibility forms a barrier to the adoption of subdivision for CAD applications. Motivated by the search for NURBS-compatible subdivision schemes, we present a non-uniform subdivision algorithm for B-splines in the spirit of the uniform Lane-Ri...

Solving linear elasticity problems using standard finite element methods, different locking phenomena can occur. In order to counteract these effects, mixed methods or formulations higher approximation orders be employed, for instance. As a consequence, this leads an increased computational effort. Hence, selective elevation of in decisive directions within purely displacement-based formulation...

In mathematics curves are typically defined as the images of continuous real functions (parametrizations) defined on a closed interval. They can also be defined as connected one-dimensional compact subsets of points. For simple curves of finite lengths, parametrizations can be further required to be injective or even length-normalized. All of these four approaches to curves are classically equi...

In this paper, we introduce a new type of splines—polynomial splines over hierarchical T-meshes (called PHT-splines) to model geometric objects. PHT-splines are a generalization of B-splines over hierarchical T-meshes. We present the detailed construction process of spline basis functions over T-meshes which have the same important properties as B-splines do, such as nonnegativity, local suppor...

In this paper, we extend the method of Scott and Barreto and present an explicit and simple algorithm to generate families of generalized MNT elliptic curves. Our algorithm allows us to obtain all families of generalized MNT curves with any given cofactor. Then, we analyze the complex multiplication equations of these families of curves and transform them into generalized Pell equation. As an e...

A new kind of NURBS representation for periodic curves is introduced. The method for periodic curves is extended to derive a compact and symmetric representation of the sphere or the ellipsoid using a piecewise bi-quadratic NURBS surface with only eight distinct control vertices.

The purpose of this study is the dimensioning of the cylindrical mixing chamber of a compressible fluid ejector used in particular in sugar refineries for degraded vapor re-compression at the calandria exit, during the evaporation phase. The method used, known as the “integral” or “thermodynamic model”, is based on the model of the one-dimensional isentropic flow of perfect gases with the addit...