Non-negative moment fitting quadrature rules for fictitious domain methods

Quadrature Rules for Fuzzy Integrals

Weighted Quadrature Rules for Finite Element Methods

We discuss the numerical integration of polynomials times exponential weighting functions arising from multiscale finite element computations. The new rules are more accurate than standard quadratures and are better suited to existing codes than formulas computed by symbolic integration. We test our approach in a multiscale finite element method for the 2D reaction-diffusion equation. Standard ...

Quadrature rules for rational functions

It is shown how recent ideas on rational Gauss-type quadrature rules can be extended to Gauss-Kronrod, Gauss-Turr an, and Cauchy principal value quadrature rules. Numerical examples illustrate the advantages in accuracy thus achievable. 0. Introduction The idea of constructing quadrature rules that are exact for rational functions with prescribed poles, rather than for polynomials, has received...

Elastostatic, Acoustic and Time-reversed Simulation of Bones by Non-standard Fictitious Domain Methods

In recent years, non-standard fictitious domain techniques [1] like the Finite Cell Method (FCM) have gained increasing interest in the context of high order methods or the integration of engineering design and numerical analysis [2]. One of the most important advantages of these methods compared to mesh-based finite element schemes is the possibility to circumvent any time-consuming mesh gener...

Weighted quadrature rules with binomial nodes

In this paper, a new class of a weighted quadrature rule is represented as --------------------------------------------  where  is a weight function,  are interpolation nodes,  are the corresponding weight coefficients and denotes the error term. The general form of interpolation nodes are considered as   that  and we obtain the explicit expressions of the coefficients  using the q-...