相关论文: Solving the Maxwell equations by the Chebyshev met…

We present a strategy for solving time-dependent problems on grids with local refinements in time using different time steps in different regions of space. We discuss and analyze two conservative approximations based on finite volume with…

For a function that is analytic on and around an interval, Chebyshev polynomial interpolation provides spectral convergence. However, if the function has a singularity close to the interval, the rate of convergence is near one. In these…

The finite-difference time-domain (FDTD) method is a well established method for solving the time evolution of Maxwell's equations. Unfortunately the scheme introduces numerical dispersion and therefore phase and group velocities which…

In this paper, we derive optimality conditions (Chebyshev approximation) for multivariate functions. The theory of Chebyshev (uniform) approximation for univariate functions is very elegant. The optimality conditions are based on the notion…

Both unconstrained and constrained minimax single facility location problems are considered in multidimensional space with Chebyshev distance. A new solution approach is proposed within the framework of idempotent algebra to reduce the…

We propose and analyze a general framework for space-time finite element methods that is based on least-squares finite element methods for solving a first-order reformulation of the thick parabolic obstacle problem. Discretizations based on…

In this paper, a novel sixth order energy-conserved method is proposed for solving the three-dimensional time-domain Maxwell's equations. The new scheme preserves five discrete energy conservation laws, three momentum conservation laws,…

We propose a solution to a time-varying variant of Markov Decision Processes which can be used to address decision-theoretic planning problems for autonomous systems operating in unstructured outdoor environments. We explore the time…

In this paper, using a pseudospectral approach, we develop operational matrices based on the shifted Chebyshev polynomials to approximate numerically Caputo fractional derivatives and Riemann-Liouville fractional integrals. In order to make…

Solving feasibility problems is a central task in mathematics and the applied sciences. One particularly successful method is the Douglas-Rachford algorithm. In this paper, we provide many new conditions sufficient for finite convergence.…

We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…

A singularly perturbed linear system of second order partial differential equations of parabolic reaction-diffusion type with given initial and boundary conditions is considered. The leading term of each equation is multiplied by a small…

The stepwise coupled-mode model is a classic approach for solving range-dependent sound propagation problems. Existing coupled-mode programs have disadvantages such as high computational cost, weak adaptability to complex ocean environments…

We present both, theory and an algorithm for solving time-harmonic wave problems in a general setting. The time-harmonic solutions will be achieved by computing time-periodic solutions of the original wave equations. Thus, an exact…

A new splitting is proposed for solving the Vlasov-Maxwell system. This splitting is based on a decomposition of the Hamiltonian of the Vlasov-Maxwell system and allows for the construction of arbitrary high order methods by composition…

We consider discrete linear Chebyshev approximation problems in which the unknown parameters of linear function are fitted by minimizing the maximum absolute deviation of errors. Such problems find application in the solution of…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

A multi-step extended maximum residual Kaczmarz method is presented for the solution of the large inconsistent linear system of equations by using the multi-step iterations technique. Theoretical analysis proves the proposed method is…

We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…

The Discontinuous Galerkin time-domain method is well suited for adaptive algorithms to solve the time-domain Maxwell's equations and depends on robust and economically computable drivers. Adaptive algorithms utilize local indicators to…