Force Computation for Dielectrics Using Shape Calculus
-
Piyush Panchal
,
Ning Ren
Abstract
We are concerned with the numerical computation of electrostatic forces/torques in only piece-wise homogeneous materials using the boundary element method (BEM). Conventional force formulas based on the Maxwell stress tensor yield functionals that fail to be continuous on natural trace spaces. Thus their use in conjunction with BEM incurs slow convergence and low accuracy. We employ the remedy discovered in [P. Panchal and R. Hiptmair, Electrostatic force computation with boundary element methods, SMAI J. Comput. Math. 8 (2022), 49–74]. Motivated by the virtual work principle which is interpreted using techniques of shape calculus, and using the adjoint method from shape optimization, we derive stable interface-based force functionals suitable for use with BEM. This is done in the framework of single-trace direct boundary integral equations for second-order transmission problems. Numerical tests confirm the fast asymptotic convergence and superior accuracy of the new formulas for the computation of total forces and torques.
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Recent Advances in Boundary Element Methods
- Fast Barrier Option Pricing by the COS BEM Method in Heston Model (with Matlab Code)
- Bernoulli Free Boundary Problems Under Uncertainty: The Convex Case
- CVEM-BEM Coupling for the Simulation of Time-Domain Wave Fields Scattered by Obstacles with Complex Geometries
- Developments on the Stability of the Non-symmetric Coupling of Finite and Boundary Elements
- Coupling of Finite and Boundary Elements for Singularly Nonlinear Transmission and Contact Problems
- BEM-Based Magnetic Field Reconstruction by Ensemble Kálmán Filtering
- Force Computation for Dielectrics Using Shape Calculus
- A Time-Adaptive Space-Time FMM for the Heat Equation
- Integral Representations and Quadrature Schemes for the Modified Hilbert Transformation
- High-Order Compact Finite Difference Methods for Solving the High-Dimensional Helmholtz Equations
- A Posteriori Error Estimates for Darcy–Forchheimer’s Problem
- Convergence of a Finite Difference Scheme for a Flame/Smoldering-Front Evolution Equation and Its Application to Wavenumber Selection
Artikel in diesem Heft
- Frontmatter
- Recent Advances in Boundary Element Methods
- Fast Barrier Option Pricing by the COS BEM Method in Heston Model (with Matlab Code)
- Bernoulli Free Boundary Problems Under Uncertainty: The Convex Case
- CVEM-BEM Coupling for the Simulation of Time-Domain Wave Fields Scattered by Obstacles with Complex Geometries
- Developments on the Stability of the Non-symmetric Coupling of Finite and Boundary Elements
- Coupling of Finite and Boundary Elements for Singularly Nonlinear Transmission and Contact Problems
- BEM-Based Magnetic Field Reconstruction by Ensemble Kálmán Filtering
- Force Computation for Dielectrics Using Shape Calculus
- A Time-Adaptive Space-Time FMM for the Heat Equation
- Integral Representations and Quadrature Schemes for the Modified Hilbert Transformation
- High-Order Compact Finite Difference Methods for Solving the High-Dimensional Helmholtz Equations
- A Posteriori Error Estimates for Darcy–Forchheimer’s Problem
- Convergence of a Finite Difference Scheme for a Flame/Smoldering-Front Evolution Equation and Its Application to Wavenumber Selection
