Related papers: Spectral Formulation of the Elastodynamic Boundary…
The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…
The interactions between dislocations and interface/grain boundaries, including dislocation absorption, transmission, and reflection, have garnered significant attention from the research community for their impact on the mechanical…
We generalize ideas in the recent literature and develop new ones in order to propose a general class of contour integral methods for linear convection-diffusion PDEs and in particular for those arising in finance. These methods aim to…
We investigate the transition radiation on a periodically deformed interface between two dielectric media. Under the assumption that the dielectric permittivities of the media are close, a formula is derived for the spectral-angular…
We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the Cartesian components of the electric, E and…
We develop a fast method for computing the electrostatic energy and forces for a collection of charges in doubly-periodic slabs with jumps in the dielectric permittivity at the slab boundaries. Our method achieves spectral accuracy by using…
Elasticity theory provides an accurate description of the long-wavelength vibrational dynamics of homogeneous crystalline solids, and with supplemental boundary conditions on the displacement field can also be applied to abrupt…
We describe examples of drastic truncations of conformal bootstrap equations encoding much more information than that obtained by a direct numerical approach. A three-term truncation of the four point function of a free scalar in any space…
In this paper, we consider band-structure calculations governed by the Helmholtz or Maxwell equations in piecewise homogeneous periodic materials. Methods based on boundary integral equations are natural in this context, since they…
Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or…
The simulation of certain flow problems requires a means for modeling a free fluid surface; examples being viscoelastic die swell or fluid sloshing in tanks. In a finite-element context, this type of problem can, among many other options,…
The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…
This paper proposes a Cartesian grid-based boundary integral method for efficiently and stably solving two representative moving interface problems, the Hele-Shaw flow and the Stefan problem. Elliptic and parabolic partial differential…
This paper is concerned with boundary integral equation methods for solving the two-dimensional fluid-solid interaction problem. We reduce the problem to three differential systems of boundary integral equations via direct and indirect…
In this paper, new boundary differential equations for the two-dimensional exterior scattering problem have been derived. It has been shown that the Helmholtz equation can be reduced to an inhomogeneous Bessel's equation in a body-fitted…
In this paper, new results on convolution of spectral components in binary fields have been presented for combiatorial sequences. A novel method of convolution of DFT points through Chinese Remainder Theorem (CRT) is presented which has…
This articles first investigates boundary integral operators for the three-dimensional isotropic linear elasticity of a biphasic model with piecewise constant Lam\'e coefficients in the form of a bounded domain of arbitrary shape surrounded…
The explicit form of the interface equation of motion derived assuming a minimal surface is extended to general bicontinuous interfaces that appear in the diffusion limited stage of the phase separation process of binary mixtures. The…
The immersed boundary (IB) method has been used as a means to simulate fluid-membrane interactions in a wide variety of biological and engineering applications. Although the numerical convergence of the method has been empirically verified,…
The immersed boundary-finite element method (IBFE) is an approach to describing the dynamics of an elastic structure immersed in an incompressible viscous fluid. In this formulation, there are discontinuities in the pressure and viscous…