Related papers: EXPODE -- Advanced Exponential Time Integration To…
We introduce the smt toolbox for Matlab. It implements optimized storage and fast arithmetics for circulant and Toeplitz matrices, and is intended to be transparent to the user and easily extensible. It also provides a set of test matrices,…
The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn--Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches,…
Matrix exponential discriminant analysis (EDA) is a generalized discriminant analysis method based on matrix exponential. It can essentially overcome the intrinsic difficulty of small sample size problem that exists in the classical linear…
Computational chemical combustion problems are known to be stiff, and are typically solved with implicit time integration methods. A novel exponential time integrator, EPI3V, is introduced and applied to a spatially homogeneous isobaric…
This article introduces a general purpose framework and software to approximate partial differential equations (PDEs). The sparsity patterns of finite element discretized operators is identified automatically using the tools from…
Explicit step-truncation tensor methods have recently proven successful in integrating initial value problems for high-dimensional partial differential equations (PDEs). However, the combination of non-linearity and stiffness may introduce…
We compare exponential-type integrators for the numerical time-propagation of the equations of motion arising in the multi-configuration time-dependent Hartree-Fock method for the approximation of the high-dimensional multi-particle…
This paper is a survey on exponential integrators to solve cubic-quintic complex Ginzburg-Landau equations and related stiff problems. In particular, we are interested in accurate computation near the pulsating and exploding soliton…
MATLAB(R) releases over the last 3 years have witnessed a continuing growth in the dynamic modeling capabilities offered by the System Identification Toolbox(TM). The emphasis has been on integrating deep learning architectures and training…
A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The…
Phase-field simulations are a practical but also expensive tool to calculate microstructural evolution. This work aims to compare explicit time integrators for a broad class of phase-field models involving coupling between the phase-field…
The efficient numerical solution of many kinetic models in plasma physics is impeded by the stiffness of these systems. Exponential integrators are attractive in this context as they remove the CFL condition induced by the linear part of…
We present a MATLAB package called the Pha-sorArray Toolbox that has been developed to make harmonic analysis and control methods both practical and user-friendly. The toolbox adopts an object-oriented architecture that enables intuitive…
Differential equations are fundamental to modeling dynamic systems in physics, engineering, biology, and economics. While analytical solutions are ideal, most real-world problems necessitate numerical approaches. This study conducts a…
In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…
In this paper we extend the polynomial time integration framework to include exponential integration for both partitioned and unpartitioned initial value problems. We then demonstrate the utility of the exponential polynomial framework by…
Exponential integrators that use Krylov approximations of matrix functions have turned out to be efficient for the time-integration of certain ordinary differential equations (ODEs). This holds in particular for linear homogeneous ODEs,…
The time integration of semilinear parabolic problems by exponential methods of different kinds is considered. A new algorithm for the implementation of these methods is proposed. The algorithm evaluates the operators required by the…
A local approach to the time integration of PDEs by exponential methods is proposed, motivated by theoretical estimates by A.Iserles on the decay of off-diagonal terms in the exponentials of sparse matrices. An overlapping domain…
In this paper, we present PIETOOLS, a MATLAB toolbox for the construction and handling of Partial Integral (PI) operators. The toolbox introduces a new class of MATLAB object, opvar, for which standard MATLAB matrix operation syntax (e.g.…