Related papers: Training and Projecting: A Reduced Basis Method Em…
This paper reports a detailed description of the equivalent linear two-body method for the many body problem, which is based on an approximate reduction of the many-body Schroedinger equation by the use of a variational principle. To test…
Physics-governed models are increasingly paired with machine learning for accelerated predictions, yet most "physics--informed" formulations treat the governing equations as a penalty loss whose scale and meaning are set by heuristic…
Simulating quantum systems in a finite volume is a powerful theoretical tool to extract information about them. Real-world properties of the system are encoded in how its discrete energy levels change with the size of the volume. This…
We present a reduced basis method for cheaply constructing (possibly rough) approximations to the nodal basis functions of the virtual element space, and propose to use such approximations for the design of the stabilization term in the…
We present an approach to accelerate real-space electronic structure methods several fold, without loss of accuracy, by reducing the dimension of the discrete eigenproblem that must be solved. To accomplish this, we construct an efficient,…
Numerical simulations are a valuable research and layout tool for fluid flow problems, yet repeated evaluations of parametrized problems, necessary to solve optimization problems, can be very costly. One option to speed up this process is…
We consider the computation of averaged coefficients for the homogenization of elliptic partial differential equations. In this problem, like in many multiscale problems, a large number of similar computations parametrized by the…
We present an overview of the evolution of ab initio methods for few-nucleon systems with A \ge 4, tracing the progress made that today allows precision calculations for these systems. First a succinct description of the diverse approaches…
We consider the elastic scattering problem by multiple disjoint arcs or \emph{cracks} in two spatial dimensions. A key aspect of our approach lies in the parametric description of each arc's shape, which is controlled by a potentially…
We present a reduced basis approach to solve the convected Helmholtz equation with several physical parameters. Physical parameters characterize the aeroacoustic wave propagation in terms of the wave and Mach numbers. We compute solutions…
Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…
In this contribution, we are concerned with parameter optimization problems that are constrained by multiscale PDE state equations. As an efficient numerical solution approach for such problems, we introduce and analyze a new relaxed and…
This work applies a reduced basis method to study the continuum physics of a finite quantum system -- either few or many-body. Specifically, I develop reduced-order models, or emulators, for the underlying inhomogeneous Schr\"{o}dinger…
Within the reduced basis methods approach, an effective low-dimensional subspace of a quantum many-body Hilbert space is constructed in order to investigate, e.g., the ground-state phase diagram. The basis of this subspace is built from…
In this paper, we propose a certified reduced basis (RB) method for quasilinear elliptic problems together with its application to nonlinear magnetostatics equations, where the later model permanent magnet synchronous motors (PMSM). The…
A bottleneck for computational lithography and optical metrology are long computational times for near field simulations. For design, optimization, and inverse scatterometry usually the same basic layout has to be simulated multiple times…
The reduced basis method is a powerful model reduction technique designed to speed up the computation of multiple numerical solutions of parametrized partial differential equations. We consider a quantity of interest, which is a linear…
This paper proposes and tests the first-ever reduced basis warm-start iterative method for the parametrized linear systems, exemplified by those discretizing the parametric partial differential equations. Traditional iterative methods are…
We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary…
Computationally intractable tasks are often encountered in physics and optimization. Such tasks often comprise a cost function to be optimized over a so-called feasible set, which is specified by a set of constraints. This may yield, in…