In this paper, we propose a new method for parameterizing a contractible domain (called the computational domain) which is defined by its boundary. Using a sequence of harmonic maps, we first build a mapping from the computational domain to the parameter domain, i.e., the unit square or unit cube. Then we parameterize the original domain by spline approximation of the inverse mapping. Numerical...

This paper proposes a method of constructing a dynamic model of a ventricle based on isogeometric simulation so as to diagnose cardiac disease more accurately. Isogeometric simulation is an accurate simulation technology based on NURBS, which has evolved into an essential tool for a semi-analytical representation of geometric entities. Especially, a new method of moving control points is used t...

We consider isogeometric functions and their derivatives. Given a geometry mapping, which is defined by an n-dimensional NURBS patch in R, an isogeometric function is obtained by composing the inverse of the geometry mapping with a NURBS function in the parameter domain. Hence an isogeometric function can be represented by a NURBS parametrization of its graph. We take advantage of the projectiv...

In this work we address the complexity problem of the isogeometric Boundary Element Method by proposing a collocation scheme for practical problems in linear elasticity and the application of hierarchical matrices. For mixed boundary value problems, a block system of matrices – similar to Galerkin formulations – is constructed allowing an effective application of that matrix format. We introduc...

A variational formulation and numerical implementation of the phase-field models for shape memory alloys using distributed computing are reported in the paper. The numerical implementation is based on the isogeometric analysis framework, constituting the rich NURBS basis functions. The phase field models are developed using the strain based order parameter and the Ginzburg-Landau theory. The fo...