Computational aspects of the ultra-weak variational formulation

Authors:
Tomi Huttunen;Peter Monk;Jari P. Kaipio
Affiliations:
Department of Applied Physics, University of Kuopio, P.O. Box 1627, 70211 Kuopio, Finland;Department of Mathematical Sciences, University of Delaware, Newark, Delaware;Department of Applied Physics, University of Kuopio, P.O. Box 1627, 70211 Kuopio, Finland
Venue:
Journal of Computational Physics
Year:
2002

Citing 5
Cited 19

BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems

SIAM Journal on Scientific and Statistical Computing
Galerkin/least-squares finite element methods for the reduced wave equation with non-reflecting boundary conditions in unbounded domains

Computer Methods in Applied Mechanics and Engineering
Finite Element Solution of the Helmholtz Equation with High Wave Number Part II: The h-p Version of the FEM

SIAM Journal on Numerical Analysis
A domain decomposition method for the Helmholtz equation and related optimal control problems

Journal of Computational Physics
Application of an Ultra Weak Variational Formulation of Elliptic PDEs to the Two-Dimensional Helmholtz Problem

SIAM Journal on Numerical Analysis

Induction heating processes optimization a general optimal control approach

Journal of Computational Physics
Feedforward and feedback control of ultrasound surgery

Applied Numerical Mathematics
Plane wave decomposition in the unit disc: convergence estimates and computational aspects

Journal of Computational and Applied Mathematics
Solving Maxwell's equations using the ultra weak variational formulation

Journal of Computational Physics
A mixed hybrid formulation based on oscillated finite element polynomials for solving Helmholtz problems

Journal of Computational and Applied Mathematics
Discontinuous Galerkin methods with plane waves for time-harmonic problems

Journal of Computational Physics
An ultra-weak method for acoustic fluid-solid interaction

Journal of Computational and Applied Mathematics
Model reduction in state identification problems with an application to determination of thermal parameters

Applied Numerical Mathematics
Feedforward and feedback control of ultrasound surgery

Applied Numerical Mathematics
Convergence analysis of non-conforming Trigonometric Finite Wave Elements

Journal of Computational and Applied Mathematics
A comparison of NRBCs for PUFEM in 2D Helmholtz problems at high wave numbers

Journal of Computational and Applied Mathematics
Locally enriched finite elements for the Helmholtz equation in two dimensions

Computers and Structures
Some numerical aspects of the PUFEM for efficient solution of 2D Helmholtz problems

Computers and Structures
Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the $p$-Version

SIAM Journal on Numerical Analysis
Analysis of the DPG Method for the Poisson Equation

SIAM Journal on Numerical Analysis
Challenges in computer applications for ship and floating structure design and analysis

Computer-Aided Design
A Galerkin least squares method for time harmonic Maxwell equations using Nédélec elements

Journal of Computational Physics
Time-independent hybrid enrichment for finite element solution of transient conduction-radiation in diffusive grey media

Journal of Computational Physics
The ultra weak variational formulation of thin clamped plate problems

Journal of Computational Physics

Quantified Score

Hi-index	31.48

Visualization

Abstract

The ultra-weak variational formulation (UWVF) approach has been proposed as an effective method for solving Helmholtz problems with high wave numbers. However, for coarse meshes the method can suffer from instability. In this paper we consider computational aspects of the ultra-weak variational formulation for the inhomogeneous Helmholtz problem. We introduce a method to improve the UWVF scheme and we compare iterative solvers for the resulting linear system. Computations for the acoustic transmission problem in 2D show that the new approach enables Helmholtz problems to be solved on a relatively coarse mesh for a wide range of wave numbers.