Search results for "MathematicsofComputing_NUMERICALANALYSIS"
showing 10 items of 149 documents
Reservoir Computing with Random Skyrmion Textures
2020
The Reservoir Computing (RC) paradigm posits that sufficiently complex physical systems can be used to massively simplify pattern recognition tasks and nonlinear signal prediction. This work demonstrates how random topological magnetic textures present sufficiently complex resistance responses for the implementation of RC as applied to A/C current pulses. In doing so, we stress how the applicability of this paradigm hinges on very general dynamical properties which are satisfied by a large class of physical systems where complexity can be put to computational use. By harnessing the complex resistance response exhibited by random magnetic skyrmion textures and using it to demonstrate pattern…
A Lagrange Multiplier Based Domain Decomposition Method for the Solution of a Wave Problem with Discontinuous Coefficients
2008
In this paper we consider the numerical solution of a linear wave equation with discontinuous coefficients. We divide the computational domain into two subdomains and use explicit time difference scheme along with piecewise linear finite element approximations on semimatching grids. We apply boundary supported Lagrange multiplier method to match the solution on the interface between subdomains. The resulting system of linear equations of the “saddle-point” type is solved efficiently by a conjugate gradient method.
Jacobian-free approximate solvers for hyperbolic systems: Application to relativistic magnetohydrodynamics
2017
Abstract We present recent advances in PVM (Polynomial Viscosity Matrix) methods based on internal approximations to the absolute value function, and compare them with Chebyshev-based PVM solvers. These solvers only require a bound on the maximum wave speed, so no spectral decomposition is needed. Another important feature of the proposed methods is that they are suitable to be written in Jacobian-free form, in which only evaluations of the physical flux are used. This is particularly interesting when considering systems for which the Jacobians involve complex expressions, e.g., the relativistic magnetohydrodynamics (RMHD) equations. On the other hand, the proposed Jacobian-free solvers hav…
A Perturbation Approach to Continuous-Time Portfolio Selection Under Stochastic Investment Opportunities
2013
This paper studies portfolio selection in continuous-time models with stochastic investment opportunities. We consider asset allocation problems where preferences are specified as power utility derived from terminal wealth as well as consumption-savings problems with recursive utility Epstein-Zin preferences. The paper approximates the associated dynamic programming problem by perturbing the coefficients of the stochastic dynamics. We represent the Hamilton-Jacobi-Bellman equation as a series of partial differential equations that can be solved iteratively in closed-form through computer algebra software, at any desired accuracy.
Comparison of parallel implementation of some multi-level Schwarz methods for singularly perturbed parabolic problems
1999
Abstract Parallel multi-level algorithms combining a time discretization and an overlapping domain decomposition technique are applied to the numerical solution of singularly perturbed parabolic problems. Two methods based on the Schwarz alternating procedure are considered: a two-level method with auxiliary “correcting” subproblems as well as a three-level method with auxiliary “predicting” and “correcting” subproblems. Moreover, modifications of the methods using time extrapolation on subdomain interfaces are investigated. The emphasis is given to the description of the algorithms as well as their computer realization on a distributed memory multiprocessor computer. Numerical experiments …
Neural network approach to solving fuzzy nonlinear equations using Z-numbers
2020
In this article, the fuzzy property is described by means of the Z-number as the coefficients and variables of the fuzzy equations. This alteration for the fuzzy equation is appropriate for system modeling with Z-number parameters. In this article, the fuzzy equation with Z-number coefficients and variables is tended to be used as the models for the uncertain systems. The modeling issue related to the uncertain system is to obtain the Z-number coefficients and variables of the fuzzy equation. Nevertheless, it is extremely hard to get the Z-number coefficients of the fuzzy equations. In this article, in order to model the uncertain nonlinear systems, a novel structure of the multilayer neura…
Large-x Analysis of an Operator-Valued Riemann–Hilbert Problem
2015
International audience; The purpose of this paper is to push forward the theory of operator-valued Riemann-Hilbert problems and demonstrate their effectiveness in respect to the implementation of a non-linear steepest descent method a la Deift-Zhou. In this paper, we demonstrate that the operator-valued Riemann-Hilbert problem arising in the characterization of so-called c-shifted integrable integral operators allows one to extract the large-x asymptotics of the Fredholm determinant associated with such operators.
Maximal regularity via reverse Hölder inequalities for elliptic systems of n-Laplace type involving measures
2008
In this note, we consider the regularity of solutions of the nonlinear elliptic systems of n-Laplacian type involving measures, and prove that the gradients of the solutions are in the weak Lebesgue space Ln,∞. We also obtain the a priori global and local estimates for the Ln,∞-norm of the gradients of the solutions without using BMO-estimates. The proofs are based on a new lemma on the higher integrability of functions.
Equilibrium real gas computations using Marquina's scheme
2003
Marquina's approximate Riemann solver for the compressible Euler equations for gas dynamics is generalized to an arbitrary equilibrium equation of state. Applications of this solver to some test problems in one and two space dimensions show the desired accuracy and robustness
On a step method and a propagation of discontinuity
2019
In this paper we analyze how to compute discontinuous solutions for functional differential equations, looking at an approach which allows to study simultaneously continuous and discontinuous solutions. We focus our attention on the integral representation of solutions and we justify the applicability of such an approach. In particular, we improve the step method in such a way to solve a problem of vanishing discontinuity points. Our solutions are considered as regulated functions.