相关论文: A low-rank, high-order implicit-explicit integrato…
Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper…
We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical…
Folding grid value vectors of size $2^L$ into $L$th order tensors of mode sizes $2\times \cdots\times 2$, combined with low-rank representation in the tensor train format, has been shown to lead to highly efficient approximations for…
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…
We present a finite-difference integration algorithm for solution of a system of differential equations containing a diffusion equation with nonlinear terms. The approach is based on Crank-Nicolson method with predictor-corrector algorithm…
We study a multigrid method for solving large linear systems of equations with tensor product structure. Such systems are obtained from stochastic finite element discretization of stochastic partial differential equations such as the…
Computing numerical solutions of the thermal radiative transfer equations on a finely resolved grid can be costly due to high computational and memory requirements. A numerical reduced order method that has recently been applied to a wide…
We introduce a dynamical low-rank method to reduce the computational complexity for solving the multi-scale multi-dimensional linear transport equation. The method is based on a macro-micro decomposition of the equation. The proposed…
We devise a space-time tensor method for the low-rank approximation of linear parabolic evolution equations. The proposed method is a stable Galerkin method, uniformly in the discretization parameters, based on a Minimal Residual…
We present a novel tensor interpolation algorithm for the time integration of nonlinear tensor differential equations (TDEs) on the tensor train and Tucker tensor low-rank manifolds, which are the building blocks of many tensor network…
An optimization-based approach for the Tucker tensor approximation of parameter-dependent data tensors and solutions of tensor differential equations with low Tucker rank is presented. The problem of updating the tensor decomposition is…
We propose a novel family of asymptotically stable, implicit-explicit, adaptive, time integration method (denoted with the $\theta$-method) for the solution of the fractional advection-diffusion-reaction (FADR) equations. This family of…
We present a method for solving the reaction-diffusion equation with general potential in free space. It is based on the approximation of the Feynman-Kac formula by a sequence of convolutions on sequentially diminishing grids. For…
We propose a second order exponential scheme suitable for two-component coupled systems of stiff evolutionary advection--diffusion--reaction equations in two and three space dimensions. It is based on a directional splitting of the involved…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
High-performance computing trends towards many-core systems are expected to continue over the next decade. As a result, parallel-in-time methods, mathematical formulations which exploit additional degrees of parallelism in the time…
Segregated Runge-Kutta (SRK) schemes are time integration methods for the incompressible Navier-Stokes equations. In this approach, convection and diffusion can be independently treated either explicitly or implicitly, which in particular…
We present a new method based on functional tensor decomposition and dynamic tensor approximation to compute the solution of a high-dimensional time-dependent nonlinear partial differential equation (PDE). The idea of dynamic approximation…
In this work we propose an efficient black-box solver for two-dimensional stationary diffusion equations, which is based on a new robust discretization scheme. The idea is to formulate an equation in a certain form without derivatives with…
In this paper we continue the work on implicit-explicit (IMEX) time discretizations for the incompressible Oseen equations that we started in \cite{BGG23} (E. Burman, D. Garg, J. Guzm\`an, {\emph{Implicit-explicit time discretization for…