Related papers: A high-order partitioned solver for general multip…

Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing…

Solving large-scale Partial Differential Equations (PDEs) on complex three-dimensional geometries represents a central challenge in scientific and engineering computing, often impeded by expensive pre-processing stages and substantial…

We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for…

Discrete gradient methods are geometric integration techniques that can preserve the dissipative structure of gradient flows. Due to the monotonic decay of the function values, they are well suited for general convex and nonconvex…

Optimization problems become fundamentally challenging as the number of variables increases. Because the volume of the search space grows exponentially, classical algorithms frequently fail to locate the global minimum of non-convex…

In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped…

In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…

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…

In this paper, a class of arbitrarily high-order linear momentum-preserving and energy-preserving schemes are proposed, respectively, for solving the regularized long-wave equation. For the momentum-preserving scheme, the key idea is based…

We present a higher order space-time unfitted finite element method for convection-diffusion problems on coupled (surface and bulk) domains. In that way, we combine a method suggested by Heimann, Lehrenfeld, Preu{\ss} (SIAM J. Sci. Comput.…

A novel compressed matrix format is proposed that combines an adaptive hierarchical partitioning of the matrix with low-rank approximation. One typical application is the approximation of discretized functions on rectangular domains; the…

An efficient and accurate finite-element algorithm is described for the numerical solution of the incompressible Navier-Stokes (INS) equations. The new algorithm that solves the INS equations in a velocity-pressure reformulation is based on…

In this paper, a higher-order time-discretization scheme is proposed, where the iterates approximate the solution of the stochastic semilinear wave equation driven by multiplicative noise with general drift and diffusion. We employ a…

Optimization is at the heart of machine learning, statistics and many applied scientific disciplines. It also has a long history in physics, ranging from the minimal action principle to finding ground states of disordered systems such as…

We consider a mixed dimensional elliptic partial differential equation posed in a bulk domain with a large number of embedded interfaces. In particular, we study well-posedness of the problem and regularity of the solution. We also propose…

We leverage the proximal Galerkin algorithm (Keith and Surowiec, Foundations of Computational Mathematics, 2024, DOI: 10.1007/s10208-024-09681-8), a recently introduced mesh-independent algorithm, to obtain a high-order finite element…

A semi-implicit-explicit (semi-IMEX) Runge-Kutta (RK) method is proposed for the numerical integration of ordinary differential equations (ODEs) of the form $\mathbf{u}' = \mathbf{f}(t,\mathbf{u}) + G(t,\mathbf{u}) \mathbf{u}$, where…

We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are…

We propose in this paper a Proper Generalized Decomposition (PGD) solver for reduced-order modeling of linear elastodynamic problems. It primarily focuses on enhancing the computational efficiency of a previously introduced PGD solver based…

Achieving robust control and optimization in high-fidelity physics simulations is extremely challenging, especially for evolutionary systems whose solutions span vast scales across space, time, and physical variables. In conjunction with…