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We present a generative learning framework for probabilistic sampling based on an extension of the Probabilistic Learning on Manifolds (PLoM) approach, which is designed to generate statistically consistent realizations of a random vector…
A second-order face-centred finite volume method (FCFV) is proposed. Contrary to the more popular cell-centred and vertex-centred finite volume (FV) techniques, the proposed method defines the solution on the faces of the mesh (edges in two…
Poisson Surface Reconstruction is a widely-used algorithm for reconstructing a surface from an oriented point cloud. To facilitate applications where only partial surface information is available, or scanning is performed sequentially, a…
Multiplication is a fundamental operation in many applications, and multipliers are widely adopted in various circuits. However, optimizing multipliers is challenging due to the extensive design space. In this paper, we propose a multiplier…
A new approach to the solution of boundary value problems within the so-called fictitious domain methods philosophy is proposed which avoids well known shortcomings of other fictitious domain methods, including the need to generate…
We present a simple and effective multigrid-based Poisson solver of second-order accuracy in both gravitational potential and forces in terms of the one, two and infinity norms. The method is especially suitable for numerical simulations…
Fast multipole methods (FMM) were originally developed for accelerating $N$-body problems for particle-based methods. FMM is more than an $N$-body solver, however. Recent efforts to view the FMM as an elliptic Partial Differential Equation…
Evaluation of pair potentials is critical in a number of areas of physics. The classicalN-body problem has its root in evaluating the Laplace potential, and has spawned tree-algorithms, the fast multipole method (FMM), as well as kernel…
Dispersion-free ultra-high order FFT-based Maxwell solvers have recently proven to be paramount to a large range of applications, including the high-fidelity modeling of high-intensity laser-matter interactions with Particle-In-Cell (PIC)…
We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of the vector field are prescribed at the…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the fifth paper, the usual structural analysis of plates on an elastic foundation…
We introduce a numerical strategy to efficiently solve the out-of-equilibrium Dyson equation in the transient regime. By discretizing the equation into a compact matrix form and applying state-of-the-art matrix compression techniques, we…
We propose a fourth-order cut-cell method for solving Poisson's equations in three-dimensional irregular domains. Major distinguishing features of our method include (a) applicable to arbitrarily complex geometries, (b) high order…
We present a fully analytic approach for evaluating boundary integrals in two dimensions for Smoothed Particle Hydrodynamics (SPH). Conventional methods often rely on boundary particles or wall re-normalization approaches derived from…
This paper proposes an efficient algorithm for solving the Hartree--Fock equation combining a multilevel correction scheme with an adaptive refinement technique to improve computational efficiency. The algorithm integrates a multilevel…
We extend the theory of matrix completion to the case where we make Poisson observations for a subset of entries of a low-rank matrix. We consider the (now) usual matrix recovery formulation through maximum likelihood with proper…
In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary…
As part of our development of a computer code to perform 3D `constrained evolution' of Einstein's equations in 3+1 form, we discuss issues regarding the efficient solution of elliptic equations on domains containing holes (i.e., excised…
An essential ingredient of a spectral method is the choice of suitable bases for test and trial spaces. On complex domains, these bases are harder to devise, necessitating the use of domain partitioning techniques such as the spectral…
This work presents an safe and efficient methodology for autonomous indoor exploration with aerial robots using Harmonic Potential Fields (HPF). The challenge of applying HPF in complex 3D environments rests on high computational load…