Related papers: Power Grid Simulation using Matrix Exponential Met…

Low-rank methods have shown success in accelerating simulations of a collisionless plasma described by the Vlasov equation, but still rely on computationally costly linear algebra every time step. We propose a data-driven factorization…

A Krylov subspace recycling method for the efficient evaluation of a sequence of matrix functions acting on a set of vectors is developed. The method improves over the recycling methods presented in [Burke et al., arXiv:2209.14163, 2022] in…

We develop a conservative phase-space grid-adaptivity strategy for the Vlasov-Fokker-Planck equation in a planar geometry. The velocity-space grid is normalized to the thermal speed and shifted by the bulk-fluid velocity. The…

We present an iterative generalisation of the quantum subspace expansion algorithm used with a Krylov basis. The iterative construction connects a sequence of subspaces via their lowest energy states. Diagonalising a Hamiltonian in a given…

Bayesian inference for models with intractable likelihoods, such as Markov random fields, poses a fundamental computational challenge due to the tradeoff between inferential accuracy and computational cost. Various MCMC methods have been…

In the design flow of integrated circuits, chip-level verification is an important step that sanity checks the performance is as expected. Power grid verification is one of the most expensive and time-consuming steps of chip-level…

Topology control for power grid operation is a challenging sequential decision making problem because the action space grows combinatorially with the size of the grid and action evaluation through simulation is computationally expensive. We…

This note proposes an efficient preconditioner for solving linear and semi-linear parabolic equations. With the Crank-Nicholson time stepping method, the algebraic system of equations at each time step is solved with the conjugate gradient…

Krylov subspace recycling is a powerful tool for solving long series of large, sparse linear systems that change slowly. In PDE constrained shape optimization, these appear naturally, as hundreds or more optimization steps are needed with…

Fast convergent, accurate, computationally efficient, parallelizable, and robust matrix inversion and parameter estimation algorithms are required in many time-critical and accuracy-critical applications such as system identification,…

Time series aggregation is a common approach to reduce the computational complexity of large-scale energy system optimization models. However, maintaining chronological continuity between the resulting representative periods (RPs) remains a…

The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and…

The Cahn-Hilliard equation has been widely employed within various mathematical models in physics, chemistry and engineering. Explicit stabilized time stepping methods can be attractive for time integration of the Cahn-Hilliard equation,…

We describe a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods provide effective convergence acceleration and preconditioning on all…

The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a…

This paper presents a new algorithm KIOPS for computing linear combinations of $\varphi$-functions that appear in exponential integrators. This algorithm is suitable for large-scale problems in computational physics where little or no…

Dynamic simulation plays a crucial role in power system transient stability analysis, but traditional numerical integration-based methods are time-consuming due to the small time step sizes. Other semi-analytical solution methods, such as…

We consider an effective new method for solving trust-region and norm-regularization problems that arise as subproblems in many optimization applications. We show that the solutions to such subproblems effectively lie in a…

An efficient and robust linear scaling method is presented for large scale {\it ab initio} electronic structure calculations of a wide variety of materials including metals. The detailed short range and the effective long range…

The matrix exponential is a fundamental operator in scientific computing and system simulation, with applications ranging from control theory and quantum mechanics to modern generative machine learning. While Pad\'e approximants combined…