We present a novel method to perform numerical integration over curved polyhedra
enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a …

A high-order quadrature algorithm is presented for computing integrals over curved surfaces
and volumes whose geometry is implicitly defined by the level sets of (one or more) …

Combining sum factorization, weighted quadrature, and row-based assembly enables
efficient higher-order computations for tensor product splines. We aim to transfer these …

When modeling scientific and industrial problems, geometries are typically modeled by
explicit boundary representations obtained from computer-aided design software. Unfitted …

This paper presents a novel method for solving partial differential equations on three-
dimensional CAD geometries by means of immersed isogeometric discretizations that do not …

We present a novel stabilized isogeometric formulation for the Stokes problem, where the
geometry of interest is obtained via overlapping NURBS (non-uniform rational B-spline) …

We present a high-order method that provides numerical integration on volumes, surfaces,
and lines defined implicitly by two smooth intersecting level sets. To approximate the …

Immersed boundary methods are high-order accurate computational tools used to model
geometrically complex problems in computational mechanics. While traditional finite …

A new quadrature rule for 2D/3D domains is proposed. We first embed the domain in a
circumscribing square/cube and then distribute a set of Gauss points in the square/cube. A …

A high-order quadrature algorithm is presented for computing integrals over curved surfaces
and volumes whose geometry is implicitly defined by the level sets of (one or more) …