Divergence boundary conditions for vector Helmholtz equations with
    divergence constraints

Urve Kangro; Roy Nicolaides

doi:10.1051/m2an:1999148

Abstract

The idea of replacing a divergence constraint by a divergence boundary condition is investigated. The connections between the formulations are considered in detail. It is shown that the most common methods of using divergence boundary conditions do not always work properly. Necessary and sufficient conditions for the equivalence of the formulations are given.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Dhia, Anne-Sophie Bonnet-Ben Hazard, Christophe and Lohrengel, Stephanie 1999. A Singular Field Method for the Solution of Maxwell's Equations in Polyhedral Domains. SIAM Journal on Applied Mathematics, Vol. 59, Issue. 6, p. 2028.

Ricci, Paolo Lapenta, Giovanni and Brackbill, J.U. 2002. A Simplified Implicit Maxwell Solver. Journal of Computational Physics, Vol. 183, Issue. 1, p. 117.

Hazard, Christophe 2002. Numerical simulation of corner singularities: a paradox in Maxwell-like problems. Comptes Rendus Mécanique, Vol. 330, Issue. 1, p. 57.

Semenov, A. S. Kessler, H. Liskowsky, A. and Balke, H. 2006. On a vector potential formulation for 3D electromechanical finite element analysis. Communications in Numerical Methods in Engineering, Vol. 22, Issue. 5, p. 357.

Duan, Huo-Yuan Lin, Ping Saikrishnan, P. and Tan, Roger C. E. 2007. A Least-Squares Finite Element Method for the Magnetostatic Problem in A Multiply Connected Lipschitz Domain. SIAM Journal on Numerical Analysis, Vol. 45, Issue. 6, p. 2537.

Kim, Tujin and Cao, Daomin 2010. Local Exact Controllability of the Navier–Stokes Equations with the Condition on the Pressure on Parts of the Boundary. SIAM Journal on Control and Optimization, Vol. 48, Issue. 6, p. 3805.

Zhou, Dong Seibold, Benjamin Shirokoff, David Chidyagwai, Prince and Rosales, Rodolfo Ruben 2015. Meshfree Methods for Partial Differential Equations VII. Vol. 100, Issue. , p. 223.

Stark, Sebastian Semenov, Artem S. and Balke, Herbert 2015. On the boundary conditions for the vector potential formulation in electrostatics. International Journal for Numerical Methods in Engineering, Vol. 102, Issue. 11, p. 1704.

Kim, Tujin and Cao, Daomin 2015. Some properties on the surfaces of vector fields and its application to the Stokes and Navier–Stokes problems with mixed boundary conditions. Nonlinear Analysis: Theory, Methods & Applications, Vol. 113, Issue. , p. 94.

Borcea, Liliana and Nguyen, Dinh-Liem 2016. Imaging with electromagnetic waves in terminating waveguides. Inverse Problems and Imaging, Vol. 10, Issue. 4, p. 915.

Ramalingom, Delphine Cocquet, Pierre-Henri and Bastide, Alain 2018. A new interpolation technique to deal with fluid-porous media interfaces for topology optimization of heat transfer. Computers & Fluids, Vol. 168, Issue. , p. 144.

Hong, Youngjoon and Nicholls, David P. 2018. A high-order perturbation of surfaces method for vector electromagnetic scattering by doubly layered periodic crossed gratings. Journal of Computational Physics, Vol. 372, Issue. , p. 748.

Du, Zhijie Duan, Huoyuan and Liu, Wei 2020. Staggered Taylor–Hood and Fortin elements for Stokes equations of pressure boundary conditions in Lipschitz domain. Numerical Methods for Partial Differential Equations, Vol. 36, Issue. 1, p. 185.

Rosales, Rodolfo Ruben Seibold, Benjamin Shirokoff, David and Zhou, Dong 2021. High-order finite element methods for a pressure Poisson equation reformulation of the Navier–Stokes equations with electric boundary conditions. Computer Methods in Applied Mechanics and Engineering, Vol. 373, Issue. , p. 113451.

Kim, Tujin and Cao, Daomin 2021. Equations of Motion for Incompressible Viscous Fluids. p. 83.

Matsui, Kazunori 2022. A projection method for Navier–Stokes equations with a boundary condition including the total pressure. Numerische Mathematik, Vol. 152, Issue. 3, p. 663.

Tran, Quyen 2023. Advances in Inverse Problems for Partial Differential Equations. Vol. 784, Issue. , p. 119.

Ye, Lv Hu, ShengBo Xu, GuangZhao and Yan, TingTing 2023. A meshless regularized method of fundamental solution for electromagnetic scattering problems of three-dimensional perfect electric conductor targets. Engineering Analysis with Boundary Elements, Vol. 155, Issue. , p. 401.

Tran, Quyen Antil, Harbir and Díaz, Hugo 2023. Optimal control of parameterized stationary Maxwell's system: Reduced basis, convergence analysis, and a posteriori error estimates. Mathematical Control and Related Fields, Vol. 13, Issue. 1, p. 431.

Article contents

Divergence boundary conditions for vector Helmholtz equations withdivergence constraints

Abstract

Keywords

Access options

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

Divergence boundary conditions for vector Helmholtz equations withdivergence constraints

Abstract

Keywords

Access options

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests