Related papers: Biorthogonal Rosenbrock-Krylov time discretization…
This paper develops a new class of Rosenbrock-type integrators based on a Krylov space solution of the linear systems. The new family, called Rosenbrock-Krylov (Rosenbrock-K), is well suited for solving large scale systems of ODEs or…
The Rosenbrock-Krylov family of time integration schemes is an extension of Rosenbrock-W methods that employs a specific Krylov based approximation of the linear system solutions arising within each stage of the integrator. This work…
Systems driven by multiple physical processes are central to many areas of science and engineering. Time discretization of multiphysics systems is challenging, since different processes have different levels of stiffness and characteristic…
This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin…
Many complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes to resolve different components of the system, according to…
Exponential integrators are special time discretization methods where the traditional linear system solves used by implicit schemes are replaced with computing the action of matrix exponential-like functions on a vector. A very general…
In this work, we propose a new method, termed as R-CORK, for the numerical solution of large-scale rational eigenvalue problems, which is based on a linearization and on a compact decomposition of the rational Krylov subspaces corresponding…
We present an overview of randomized orthogonalization techniques that construct a well-conditioned basis whose sketch is orthonormal. Randomized orthogonalization has recently emerged as a powerful paradigm for reducing the computational…
This paper is concerned with the development and testing of advanced time-stepping methods suited for the integration of time-accurate, real-world applications of computational fluid dynamics (CFD). The performance of several time…
A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…
Simulation of geothermal systems is challenging due to coupled physical processes in highly heterogeneous media. Combining the exponential Rosenbrock--Euler and Rosenbrock-type methods with control-volume (two-point flux approximation)…
We propose a high order adaptive-rank implicit integrators for stiff time-dependent PDEs, leveraging extended Krylov subspaces to efficiently and adaptively populate low-rank solution bases. This allows for the accurate representation of…
Nonlinear and nonaffine terms in parametric partial differential equations can potentially lead to a computational cost of a reduced order model (ROM) that is comparable to the cost of the original full order model (FOM). To address this,…
In this paper, a novel augmented Lagrangian preconditioner based on global Arnoldi for accelerating the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure, these systems…
In this paper, we investigate the use of multilinear algebra for reducing the order of multidimensional linear time-invariant (MLTI) systems. Our main tools are tensor rational Krylov subspace methods, which enable us to approximate the…
Non-hydrostatic atmospheric models often use semi-implicit temporal discretisations in order to negate the time step limitation of explicitly resolving the fast acoustic and gravity waves. Solving the resulting system to machine precision…
This work is on a user-friendly reduced basis method for solving a family of parametric PDEs by preconditioned Krylov subspace methods including the conjugate gradient method, generalized minimum residual method, and bi-conjugate gradient…
A high order time stepping applied to spatial discretizations provided by the method of lines for hyperbolic conservations laws is presented. This procedure is related to the one proposed in Qiu and Shu (SIAM J Sci Comput 24(6):2185-2198,…
Discrete updates of numerical partial differential equations (PDEs) rely on two branches of temporal integration. The first branch is the widely-adopted, traditionally popular approach of the method-of-lines (MOL) formulation, in which…
A novel theoretical convergence rate estimate for a Balancing Domain Decomposition by Constraints algorithm is proven for the solution of the cardiac Bidomain model, describing the propagation of the electric impulse in the cardiac tissue.…