
A coupled discontinuous GalerkinFinite Volume framework for solving gas dynamics over embedded geometries
We present a computational framework for solving the equations of invisc...
read it

A priori error analysis of highorder LL* (FOSLL*) finite element methods
A number of nonstandard finite element methods have been proposed in re...
read it

Highorder finite element methods for nonlinear convectiondiffusion equation on timevarying domain
A highorder finite element method is proposed to solve the nonlinear co...
read it

High order methods for acoustic scattering: Coupling Farfield Expansions ABC with DeferredCorrection methods
Arbitrary high order numerical methods for timeharmonic acoustic scatte...
read it

Quadrature for Implicitlydefined Finite Element Functions on Curvilinear Polygons
H^1conforming Galerkin methods on polygonal meshes such as VEM, BEMFEM...
read it

The Multivariate SchwartzZippel Lemma
Motivated by applications in combinatorial geometry, we consider the fol...
read it

Levelset based design of Wang tiles for modelling complex microstructures
Microstructural geometry plays a critical role in a response of heteroge...
read it
HighOrder Quadrature on MultiComponent Domains Implicitly Defined by Multivariate Polynomials
A highorder 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) multivariate polynomials. The algorithm recasts the implicitly defined geometry as the graph of an implicitly defined, multivalued height function, and applies a dimension reduction approach needing only onedimensional quadrature. In particular, we explore the use of GaussLegendre and tanhsinh methods and demonstrate that the quadrature algorithm inherits their highorder convergence rates. Under the action of hrefinement with q fixed, the quadrature schemes yield an order of accuracy of 2q, where q is the onedimensional node count; numerical experiments demonstrate up to 22nd order. Under the action of qrefinement with the geometry fixed, the convergence is approximately exponential, i.e., doubling q approximately doubles the number of accurate digits of the computed integral. Complex geometry is automatically handled by the algorithm, including, e.g., multicomponent domains, tunnels, and junctions arising from multiple polynomial level sets, as well as selfintersections, cusps, and other kinds of singularities. A variety of accompanying numerical experiments demonstrates the quadrature algorithm on two and threedimensional problems, including randomly generated geometry involving multiple high curvature pieces; challenging examples involving high degree singularities such as cusps; adaptation to simplex constraint cells in addition to hyperrectangular constraint cells; and boolean operations to compute integrals on overlapping domains.
READ FULL TEXT
Comments
There are no comments yet.