Home  About us  Contact
 

Helmholtz Problem (helmholtz + problem)

Distribution by Scientific Domains
Engineering91%

Selected Abstracts

Comparison of two wave element methods for the Helmholtz problem

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2009
T. Huttunen
Abstract In comparison with low-order finite element methods (FEMs), the use of oscillatory basis functions has been shown to reduce the computational complexity associated with the numerical approximation of Helmholtz problems at high wave numbers. We compare two different wave element methods for the 2D Helmholtz problems. The methods chosen for this study are the partition of unity FEM (PUFEM) and the ultra-weak variational formulation (UWVF). In both methods, the local approximation of wave field is computed using a set of plane waves for constructing the basis functions. However, the methods are based on different variational formulations; the PUFEM basis also includes a polynomial component, whereas the UWVF basis consists purely of plane waves. As model problems we investigate propagating and evanescent wave modes in a duct with rigid walls and singular eigenmodes in an L-shaped domain. Results show a good performance of both methods for the modes in the duct, but only a satisfactory accuracy was obtained in the case of the singular field. On the other hand, both the methods can suffer from the ill-conditioning of the resulting matrix system. Copyright © 2008 John Wiley & Sons, Ltd. [source]

A hybrid-Trefftz finite element model for Helmholtz problem

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2008
K. Y. Sze
Abstract In this paper, a hybrid-Trefftz four-node quadrilateral element model is formulated for Helmholtz problem. In this model, two Helmholtz approximations are defined. The first approximation is obtained by nodal interpolation, and the second approximation is truncated from a Trefftz solution set. A hybrid variational functional is employed to enforce the equality of and other necessary conditions on the two approximations. From the numerical tests, it can be seen that the hybrid model is markedly more accurate than the conventional finite element model. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Quasi optimal finite difference method for Helmholtz problem on unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010
Daniel T. Fernandes
Abstract A quasi optimal finite difference method (QOFD) is proposed for the Helmholtz problem. The stencils' coefficients are obtained numerically by minimizing a least-squares functional of the local truncation error for plane wave solutions in any direction. In one dimension this approach leads to a nodally exact scheme, with no truncation error, for uniform or non-uniform meshes. In two dimensions, when applied to a uniform cartesian grid, a 9-point sixth-order scheme is derived with the same truncation error of the quasi-stabilized finite element method (QSFEM) introduced by Babu,ka et al. (Comp. Meth. Appl. Mech. Eng. 1995; 128:325,359). Similarly, a 27-point sixth-order stencil is derived in three dimensions. The QOFD formulation, proposed here, is naturally applied on uniform, non-uniform and unstructured meshes in any dimension. Numerical results are presented showing optimal rates of convergence and reduced pollution effects for large values of the wave number. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Coupling a mass-conserving semi-Lagrangian scheme (SLICE) to a semi-implicit discretization of the shallow-water equations: Minimizing the dependence on a reference atmosphere

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 646 2010
J. Thuburn
Abstract In a recent paper, a conservative semi-Lagrangian mass transport scheme SLICE has been coupled to a semi-implicit semi-Lagrangian scheme for the shallow-water equations. The algorithm involves the solution at each timestep of a nonlinear Helmholtz problem, which is achieved by iterative solution of a linear ,inner' Helmholtz problem; this framework, as well as the linear Helmholtz operator itself, are the same as would be used with a non-conservative interpolating semi-Lagrangian scheme for mass transport. However, in order to do this, a reference value of geopotential was introduced into the discretization. It is shown here that this results in a weak dependence of the results on that reference value. An alternative coupling is therefore proposed that preserves the same solution framework and linear Helmholtz operator but, at convergence of the nonlinear solver, has no dependence on the reference value. However, in order to maintain accuracy at large timesteps, this approach requires a modification to how SLICE performs its remapping. An advantage of removing the dependence on the reference value is that the scheme then gives consistent tracer transport. Copyright © 2010 Royal Meteorological Society and Crown Copyright. Published by John Wiley & Sons, Ltd. [source]

Comparison of two wave element methods for the Helmholtz problem

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2009
T. Huttunen
Abstract In comparison with low-order finite element methods (FEMs), the use of oscillatory basis functions has been shown to reduce the computational complexity associated with the numerical approximation of Helmholtz problems at high wave numbers. We compare two different wave element methods for the 2D Helmholtz problems. The methods chosen for this study are the partition of unity FEM (PUFEM) and the ultra-weak variational formulation (UWVF). In both methods, the local approximation of wave field is computed using a set of plane waves for constructing the basis functions. However, the methods are based on different variational formulations; the PUFEM basis also includes a polynomial component, whereas the UWVF basis consists purely of plane waves. As model problems we investigate propagating and evanescent wave modes in a duct with rigid walls and singular eigenmodes in an L-shaped domain. Results show a good performance of both methods for the modes in the duct, but only a satisfactory accuracy was obtained in the case of the singular field. On the other hand, both the methods can suffer from the ill-conditioning of the resulting matrix system. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Three-dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of mid-frequency Helmholtz problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006
Radek Tezaur
Abstract Recently, a discontinuous Galerkin finite element method with plane wave basis functions and Lagrange multiplier degrees of freedom was proposed for the efficient solution in two dimensions of Helmholtz problems in the mid-frequency regime. In this paper, this method is extended to three dimensions and several new elements are proposed. Computational results obtained for several wave guide and acoustic scattering model problems demonstrate one to two orders of magnitude solution time improvement over the higher-order Galerkin method. Copyright © 2005 John Wiley & Sons, Ltd. [source]

A variational approach to boundary elements,two dimensional Helmholtz problems

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 6 2003
Y. Kagawa
Abstract The boundary element method is a discretized version of the boundary integral equation method. The variational formulation is presented for the boundary element approach to Helmholtz problems. The numerical calculation of the eigenvalues in association with hollow waveguides demonstrates that the variational approach provides the upper and lower bounds of the eigenvalues. The drawback of the discretized system equation must be solved by a trial and error approach, which is shown to be removed by the introduction of the dual reciprocity method. Copyright © 2003 John Wiley & Sons, Ltd. [source]