In this project we numerically simulate electrophysiological models for cardiac applications by means of Isogeometric Analysis. Specifically, we aim at understanding the advantages of using high order continuous NURBS (Non-Uniform Rational B-Splines) basis functions in the approximation of the traveling waves of the action potential. As application, we consider the numerical simulations on the ...

Numerical computation of solutions for partial differential equations plays an important role in modern product development and engineering. Also, the use of computer aided design (CAD) software in the design process has become a widespread standard. These two fields are closely connected in the practical development process, but the corresponding techniques have been developed independently ov...

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...

Quadratic Powell-Sabin splines and their rational extension, the socalled NURPS surfaces, are an interesting alternative for classical tensor-product NURBS in the context of isogeometric analysis, because they allow the use of local refinements while retaining a Bspline like representation and exact description of conic sections. In this paper we present a simple and effective strategy to conve...

We use refined isogeometric analysis (rIGA) to solve generalized Hermitian eigenproblems (Ku=λMu). rIGA conserves the desirable properties of maximum-continuity (IGA) while it reduces solution cost by adding zero-continuity basis functions, which decrease matrix connectivity. As a result, enriches approximation space and interconnection between degrees freedom. compare computational costs versu...

Certain applications that analyze damping effects require the solution of quadratic eigenvalue problems (QEPs). We use refined isogeometric analysis (rIGA) to solve eigenproblems. rIGA discretization, while conserving desirable properties maximum-continuity (IGA), reduces interconnection between degrees freedom by adding low-continuity basis functions. This connectivity reduction in rIGA’s alge...

This paper presents a new isogeometric mortar contact formulation based on an extended finite element interpolation to capture physical pressure discontinuities at the contact boundary. The so called two-half-pass algorithm is employed, which leads to an unbiased formulation and, when applied to the mortar setting, has the additional advantage that the mortar coupling term is no longer present ...

We present algebraic multilevel iteration (AMLI) methods for isogeometric discretization of scalar second order elliptic problems. The construction of coarse grid operators and hierarchical complementary operators are given. Moreover, for a uniform mesh on a unit interval, the explicit representation of B-spline basis functions for a fixed mesh size h is given for p = 2, 3, 4 and for C 0-and C ...