Related papers: A simple and efficient solver for self-gravity in …
The Poisson-Boltzmann equation is widely used to model molecular electrostatics; however, it is usually solved in linearised form because the sinh nonlinearity is challenging, limiting its applicability in highly charged systems such as…
We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…
Design of modern nanostructured semiconductor devices often calls for simulation tools capable of modeling arbitrarily-shaped multiscale geometries. In this work, to this end, a discontinuous Galerkin (DG) method-based framework is…
We report an efficient algorithm using density fitting for the relativistic complete active space self-consistent field (CASSCF) method, which is significantly more stable than the algorithm previously reported by one of the authors [J. E.…
We present a fast and accurate algorithm to solve Poisson problems in complex geometries, using regular Cartesian grids. We consider a variety of configurations, including Poisson problems with interfaces across which the solution is…
We describe three approaches for computing a gravity signal from a density anomaly. The first approach consists of the classical "summation" technique, whilst the remaining two methods solve the Poisson problem for the gravitational…
Simulation of plasmas in electromagnetic fields requires numerical solution of a kinetic equation that describes the time evolution of the particle distribution function. In this paper we propose a finite volume scheme based on integral…
Computer-aided engineering techniques are indispensable in modern engineering developments. In particular, partial differential equations are commonly used to simulate the dynamics of physical phenomena, but very large systems are often…
Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method for solving the fluid equations that is commonplace in astrophysics, prized for its natural adaptivity and stability. The choice of variable to smooth in SPH has been the topic of…
We present a geometric multigrid solver for the Compact Discontinuous Galerkin method through building a hierarchy of coarser meshes using a simple agglomeration method which handles arbitrary element shapes and dimensions. The method is…
We present a generalized algorithm based on a spherical harmonics expansion method for efficient computation of the three-dimensional gravitational potential on a multi-patch grid in spherical geometry. Instead of solving for the…
We present a new quantization scheme for $2D$ gravity coupled to an $SU(2)$ principal chiral field and a dilaton; this model represents a slightly simplified version of stationary axisymmetric quantum gravity. The analysis makes use of the…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
Civan and Sliepcevich [1, 2] suggested that special matrix solver should be developed to further reduce the computing effort in applying the differential quadrature (DQ) method for the Poisson and convection-diffusion equations. Therefore,…
A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate…
This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. We leverage the proper generalized decomposition (PGD) to decompose the displacements into multiple time scales, separating the…
We present a general relativistic model of a spherical shell of matter with a perfect fluid on its surface coupled to an internal oscillator, which generalizes a model recently introduced by the authors to construct a self-gravitating…
I propose a vertex patch smoother where local problems are solved inexactly by a nested, matrix-free p-multigrid, creating a multigrid-within-multigrid framework. A single iteration of the local solver can be evaluated with…
We review the derivation of the Kac master equation model for random collisions of particles, its relationship to the Poisson process, and existing algorithms for simulating values from the marginal distribution of velocity for a single…
In geophysical fluid dynamics, the screened Poisson equation appears in the shallow-water, quasi geostrophic equations. Recently, many attempts have been made to solve those equations on the sphere using different numerical methods. These…