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We analyze a goal-oriented adaptive algorithm that aims to efficiently compute the quantity of interest $G(u^\star)$ with a linear goal functional $G$ and the solution $u^\star$ to a general second-order nonsymmetric linear elliptic partial…
We introduce a new mean-field ODE and corresponding interacting particle systems (IPS) for sampling from an unnormalized target density. The IPS are gradient-free, available in closed form, and only require the ability to sample from a…
Yen et al. (2012) advanced a direct approach for the calculation of self-gravitational force to second order accuracy based on uniform grid discretization. This method improves the accuracy of N-body calculation by using exact integration…
Reconstructing scalar fields from error-embedded gradient measurements is a fundamental linear inverse problem with broad applications in computational physics. Conventional approaches, such as Poisson-based solvers and the Green's Function…
The immersed boundary (IB) method is a non-body conforming approach to fluid-structure interaction (FSI) that uses an Eulerian description of the momentum, viscosity, and incompressibility of a coupled fluid-structure system and a…
This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions. This factorization takes the form of an approximate generalized LU…
The feedback particle filter (FPF) is an innovative, control-oriented and resampling-free adaptation of the traditional particle filter (PF). In the FPF, individual particles are regulated via a feedback gain, and the corresponding gain…
Point cloud registration is a central theme in computer vision, with alignment algorithms continuously improving for greater robustness. Commonly used methods evaluate Euclidean distances between point clouds and minimize an objective…
We consider the numerical solution of Poisson's equation on structured grids using geometric multigrid with nonstandard coarse grids and coarse level operators. We are motivated by the problem of developing high-order accurate numerical…
Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids…
The immersed boundary (IB) method is a general mathematical framework for studying problems involving fluid-structure interactions in which an elastic structure is immersed in a viscous incompressible fluid. In the IB formulation, the fluid…
For a wide range of clinical applications, such as adaptive treatment planning or intraoperative image update, feature-based deformable registration (FDR) approaches are widely employed because of their simplicity and low computational…
The dielectric response function and its inverse are crucial physical quantities in materials science. We propose an accurate and efficient strategy to invert the dielectric function matrix. The GW approximation, a powerful approach to…
The Gridding algorithm has shown great utility for reconstructing images from non-uniformly spaced samples in the Fourier domain in several imaging modalities. Due to the non-uniform spacing, some correction for the variable density of the…
The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs) on smooth surfaces, using a closest point representation…
In this work, we formulate and analyze a geometric multigrid method for the iterative solution of the discrete systems arising from the finite element discretization of symmetric second-order linear elliptic diffusion problems. We show that…
Wavelet-based grid adaptation methods use multiresolution analysis for error estimation, offering a mathematically rigorous approach to adaptive grid refinement when solving Partial Differential Equations (PDEs). However, applying these…
Accurate, global Potential Energy Surfaces (PES) expressed in sum-of-products (SOP) form are a prerequisite for efficient high-dimensional quantum dynamics simulations using the MCTDH method. This work introduces a methodology for…
Sparse-view computed tomography (CT) is a practical solution to reduce radiation dose, but the resulting ill-posed inverse problem poses significant challenges for accurate image reconstruction. Although deep learning and diffusion-based…
We propose a generalized dynamic phasor (DP) framework to analyze inverter-based resources (IBRs) connected to multi-machine systems under balanced and unbalanced conditions. It captures subsynchronous oscillations (SSOs) induced by…