Related papers: On preconditioning and solving an extended class o…
The computation time for reservoir simulation is dominated by the linear solver. The sets of linear equations which arise in reservoir simulation have two distinctive features: the problems are usually highly anisotropic, with a dominant…
It is tested whether machine learning methods can be used for preconditioning to increase the performance of the linear solver -- the backbone of the semi-implicit, grid-point model approach for weather and climate models. Embedding the…
Dynamical systems are pervasive in almost all engineering and scientific applications. Simulating such systems is computationally very intensive. Hence, Model Order Reduction (MOR) is used to reduce them to a lower dimension. Most of the…
We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel…
Recently, inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications. After the discretization, many of inverse problems are reduced to linear systems.…
Rectangular spectral collocation (RSC) methods have recently been proposed to solve linear and nonlinear differential equations with general boundary conditions and/or other constraints. The involved linear systems in RSC become extremely…
Solving multiple parametrised related systems is an essential component of many numerical tasks, and learning from the already solved systems will make this process faster. In this work, we propose a novel probabilistic linear solver over…
Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set…
The solution of systems of linear(ized) equations lies at the heart of many problems in Scientific Computing. In particular for systems of large dimension, iterative methods are a primary approach. Stationary iterative methods are generally…
The novel contribution of this paper relies in the proposal of a fully implicit numerical method designed for nonlinear degenerate parabolic equations, in its convergence/stability analysis, and in the study of the related computational…
Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and…
Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design…
Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with…
We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize…
When an iterative method is applied to solve the linear equation system in interior point methods (IPMs), the attention is usually placed on accelerating their convergence by designing appropriate preconditioners, but the linear solver is…
Many problems in optimization theory are strongly nonlinear in the traditional sense but possess a hidden linear structure over suitable idempotent semirings. After an overview of `Idempotent Mathematics' with an emphasis on matrix theory,…
Large linear systems are ubiquitous in modern computational science and engineering. The main recipe for solving them is the use of Krylov subspace iterative methods with well-designed preconditioners. Recently, GNNs have been shown to be a…
We consider the parallel-in-time solution of hyperbolic partial differential equation (PDE) systems in one spatial dimension, both linear and nonlinear. In the nonlinear setting, the discretized equations are solved with a preconditioned…
In this work, in the context of Linear and Quadratic Programming, we interpret Primal Dual Regularized Interior Point Methods (PDR-IPMs) in the framework of the Proximal Point Method. The resulting Proximal Stabilized IPM (PS-IPM) is…
We present an efficient preconditioner for linear problems $A x=y$. It guarantees monotonic convergence of the memory-efficient fixed-point iteration for all accretive systems of the form $A = L + V$, where $L$ is an approximation of $A$,…