Related papers: Generating Converging Eigenenergy Bounds for Multi…
Moment based methods have produced efficient multiscale quantization algorithms for solving singular perturbation/strong coupling problems. One of these, the Eigenvalue Moment Method (EMM), developed by Handy et al (Phys. Rev. Lett.{\bf…
Although the Christoffel-Darboux representation (CDR) plays an important role within the theory of orthogonal polynomials, and many important bosonic and fermionic multidimensional Schrodinger equation systems can be transformed into a…
The Eigenvalue Moment Method (EMM), Handy (2001), Handy and Wang (2001)) is applied to the $H_\alpha \equiv P^2 + iX^3 + i\alpha X$ Hamiltonian, enabling the algebraic/numerical generation of converging bounds to the complex energies of the…
A previously developed quantum reduced-order model is revised and applied, together with the domain decomposition, to develop the quantum element method (QEM), a methodology for fast and accurate simulation of quantum eigenvalue problems.…
There continues to be great interest in understanding quasi-exactly solvable (QES) systems. In one dimension, QES states assume the form $\Psi(x) =x^\gamma P_d(x) {\cal A}(x)$, where ${\cal A}(x) > 0$ is known in closed form, and $P_d(x)$…
Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices…
The finite element method(FEM) is applied to bound leading eigenvalues of Laplace operator over polygonal domain. Compared with classical numerical methods, most of which can only give concrete eigenvalue bounds over special domain of…
The peridynamic theory brings advantages in dealing with discontinuities, dynamic loading, and non-locality. The integro-differential formulation of peridynamics poses challenges to numerical solutions of complicated and practical problems.…
Many quantum systems admit an explicit analytic Fourier space expansion, besides the usual analytic Schrodinger configuration space representation. We argue that the use of weighted orthonormal polynomial expansions for the physical states…
The boundary element method (BEM) enables solving three-dimensional electromagnetic problems using a two-dimensional surface mesh, making it appealing for applications ranging from electrical interconnect analysis to the design of…
The paper outlines some recent developments of the boundary element method (BEM) that makes it more user friendly and suitable for a realistic simulation in geomechanics, especially for underground excavations and tunnelling. The…
We develop an efficient and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the regularization technique of Chen, Holst, and Xu; this technique made possible the first a…
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum)…
The Generalized Method of Moments (GMM) is a partition of unity based technique for solving electromagnetic and acoustic boundary integral equations. Past work on the GMM for electromagnetics was confined to geometries modeled by piecewise…
We use moment techniques to construct a converging hierarchy of optimization problems to lower bound the ground state energy of interacting particle systems. We approximate (from below) the infinite dimensional optimization problems in this…
This work illustrates the possibility to apply the Fast Fourier Transformation to obtain the integrals of the Boundary Element Method (BEM) on arbitrary shapes. The procedure is inspired by the technique used with great success within the…
We present two approximation methods for computing eigenfrequencies and eigenmodes of large-scale nonlinear eigenvalue problems resulting from boundary element method (BEM) solutions of some types of acoustic eigenvalue problems in…
Numerical homogenization for mechanical multiscale modeling by means of the finite element method (FEM) is an elegant way of obtaining structure-property relations, if the behavior of the constituents of the lower scale is well understood.…
The boundary element method (BEM) is an efficient numerical method for simulating harmonic wave propagation. It uses boundary integral formulations of the Helmholtz equation at the interfaces of piecewise homogeneous domains. The…
We propose a Restricted Boltzmann Machine (RBM) neural network using a quantum thermodynamics formalism and the maximization of entropy as the cost function for the optimization problem. We verify the possibility of using an entropy…