Parallel Solvers for Flexible Approximation Schemes in Multiparticle Simulation

  title={Parallel Solvers for Flexible Approximation Schemes in Multiparticle Simulation},
  author={Masha Sosonkina and Igor Tsukerman},
  booktitle={International Conference on Computational Science},
New finite difference schemes with flexible local approximation are applied to screened electrostatic interactions of spherical colloidal particles governed by the Poisson-Boltzmann equation. Local analytical approximations of the solution are incorporated directly into the scheme and yield high approximation accuracy even on simple and relatively coarse Cartesian grids. Several parallel iterative solution techniques have been tested with an emphasis on suitable parallel preconditioning for the… 
Difference Schemes with Local Numerical Bases for Multiparticle Interactions
The recently developed flexible local approximation method (FLAME) incorporates accurate local approximations of the solution into the difference scheme. When analytical approximations are too
Flexible approximation schemes with numerical and semi‐analytical bases
Purpose – The purpose of this paper is to extend the generalized finite‐difference calculus of flexible local approximation methods (FLAME) to problems where local analytical solutions are
A Hybrid CPU/GPU Approach for the Parallel Algebraic Recursive Multilevel Solver pARMS
Numerical experiments show that a promising performance improvement can be obtained using either randomized multilevel recursive preconditioning or Incomplete LU preconditionsing for large enough matrices.
The application of Trefftz-FLAME to electromagnetic wave problems
Numerical analysis of the electromagnetic fields in large, complex structures is very challenging due to the high computational overhead. Recently, it has been shown that a new method called


Parallel Generalized Finite Element Method for Magnetic Multiparticle Problems
A general-purpose parallel Schur complement solver with incomplete LU preconditioning showed excellent performance for the varying problem size, number of processors and number of particles.
Electromagnetic applications of a new finite-difference calculus
The accuracy of finite-difference analysis in electromagnetics can be qualitatively improved by employing arbitrary local approximating functions, not limited to Taylor expansion polynomials. In the
A new version of the fast multipole method for screened Coulomb interactions in three dimensions
A new version of the fast multipole method (FMM) for screened Coulomb interactions in three dimensions relies on an expansion in evanescent plane waves, with which the amount of work can be reduced to 40p2 + 6p3 operations per box.
Iterative methods for sparse linear systems
This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.
Generalized finite-element method for magnetized nanoparticles
The generalized finite-element method is applied to model self-assembly of magnetized nanoparticles. Only a regular hexahedral grid is used. The particles need not be meshed and are represented by
Method of overlapping patches for electromagnetic computation
A far-reaching generalization of the finite-element method (FEM), the method of partition of unity on overlapping patches, is applied, as an illustrative example, to a waveguide problem. No
Ewald sums for Yukawa potentials
The numerical simulation of systems involving Yukawa interaction y(r)=exp(−αr)/r (e.g., colloids, dusty plasmas,…) needs some caution in the case where the potential cannot be neglected on the