piyush panchal | Swiss Federal Institute of Technology (ETH) (original) (raw)
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Papers by piyush panchal
Computational Methods in Applied Mathematics
We are concerned with the numerical computation of electrostatic forces/torques in only piece-wis... more 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 th...
The SMAI journal of computational mathematics
In Electrostatics, it is often of interest to compute local/global forces on a body in electrosta... more In Electrostatics, it is often of interest to compute local/global forces on a body in electrostatic equilibrium. The classical formula for computing this force is a surface/volume integral, obtained using the Maxwell Stress Tensor. In the surface integral form it has some undesirable properties, affecting the accuracy when used with Boundary Element Methods. In this work, we explore a new approach for calculating the force using shape calculus, in an effort to find a stable formula on the boundary which can be used with BEM. The properties of this new formula are discussed using numerical experiments.
Computational Methods in Applied Mathematics
We are concerned with the numerical computation of electrostatic forces/torques in only piece-wis... more 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 th...
The SMAI journal of computational mathematics
In Electrostatics, it is often of interest to compute local/global forces on a body in electrosta... more In Electrostatics, it is often of interest to compute local/global forces on a body in electrostatic equilibrium. The classical formula for computing this force is a surface/volume integral, obtained using the Maxwell Stress Tensor. In the surface integral form it has some undesirable properties, affecting the accuracy when used with Boundary Element Methods. In this work, we explore a new approach for calculating the force using shape calculus, in an effort to find a stable formula on the boundary which can be used with BEM. The properties of this new formula are discussed using numerical experiments.