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We present a novel technique by which highly-segmented electrostatic configurations can be solved. The Robin Hood method is a matrix-inversion algorithm optimized for solving high density boundary element method (BEM) problems. We…
Recent progress in experimental techniques has made the quantum regime in plasmonics accessible. Since plasmons correspond to collective electron excitations, the electron-electron interaction plays an essential role in their theoretical…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
A relation between classical electrostatic fields and Schr\"odinger-like Hamiltonians is evidenced. Hence, supersymmetric quantum potentials analogous to classical electrostatic fields can be constructed. Proposing an ansatz for the…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
The scaling of the exact solution of a hyperbolic balance law generates a family of scaled problems in which the source term does not depend on the current solution. These problems are used to construct a sequence of solutions whose…
In this paper we extend analysis of the WaveHoltz iteration -- a time-domain iterative method for the solution of the Helmholtz equation. We expand the previous analysis of energy conserving problems and prove convergence of the WaveHoltz…
A discrete analysis of the phase and dissipation errors of an explicit, semi-Lagrangian spectral element method is performed. The semi-Lagrangian method advects the Lagrange interpolant according the Lagrangian form of the transport…
We derive a self-consistent local variant of the Thomas-Fermi approximation for (quasi-)two-dimensional (2D) systems by localizing the Hartree term. The scheme results in an explicit orbital-free representation of the electron density and…
Solving the wave equation is one of the most (if not the most) fundamental problems we face as we try to illuminate the Earth using recorded seismic data. The Helmholtz equation provides wavefield solutions that are dimensionally reduced,…
We propose several new nonsmooth Newton methods for solving convex composite optimization problems with polyhedral regularizers, while avoiding the computation of complicated second-order information on these functions. Under the…
In this paper the hp-version of the boundary element method is applied to the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. The underlying meshes are supposed to be quasi-uniform. We use…
Self-consistent field theory (SCFT) is one of the most widely-used framework in studying the equilibrium phase behaviors of inhomogenous polymers. For liquid crystalline polymeric systems, the main numerical challenges of solving SCFT…
The Helmholtz equation arises in the study of electromagnetic radiation, optics, acoustics, etc. In spherical coordinates, its general solution can be written as a spherical harmonic series which satisfies the radiation condition at…
Fast and accurate resolution of electromagnetic problems via the \ac{BEM} is oftentimes challenged by conditioning issues occurring in three distinct regimes: (i) when the frequency decreases and the discretization density remains constant,…
The development of numerical methods capable of simulating realistic materials with strongly correlated electrons, with controllable errors, is a central challenge in quantum many-body physics. Here we describe how a hybrid between…
This paper studies the convergence difficulty of cohesive zone models in static analysis. It is shown that an inappropriate starting point of iterations in the Newton-Raphson method is responsible for the convergence difficulty. A simple,…
We substantiate the need for account of the proper electromagnetic field of the electron in the canonical problem of hydrogen in relativistic quantum mechanics. From mathematical viewpoint, the goal is equivalent to determination of the…
We consider the numerical solution of Hamilton-Jacobi-Bellman equations arising in stochastic control theory. We introduce a class of monotone approximation schemes relying on monotone interpolation. These schemes converge under very weak…
Several newly developing hybrid imaging methods (e.g., those combining electrical impedance or optical imaging with acoustics) enable one to obtain some auxiliary interior information (usually some combination of the electrical conductivity…