Related papers: Two-dimensional Gauss--Jacobi Quadrature for Multi…
The DESC stellarator optimization code takes advantage of advanced numerical methods to search the full parameter space much faster than conventional tools. Only a single equilibrium solution is needed at each optimization step thanks to…
A deterministic-stochastic coupling scheme is developed for simulating rarefied gas flows, where the key process is the alternative solving of the macroscopic synthetic equations [Su et al., J. Comput. Phys., 407 (2020) 109245] and the…
We develop a high-order, explicit method for acoustic scattering in three space dimensions based on a combined-field time-domain integral equation. The spatial discretization, of Nystr\"om type, uses Gaussian quadrature on panels combined…
3D Gaussian Splatting is a recognized method for 3D scene representation, known for its high rendering quality and speed. However, its substantial data requirements present challenges for practical applications. In this paper, we introduce…
Modelling rarefied gas flow via the Boltzmann equation plays a vital role in many areas. Due to the high dimensionality of this kinetic equation and the coexistence of multiple characteristic scales in the transport processes, conventional…
Gaussian Splatting and its dynamic extensions are effective for reconstructing 3D scenes from 2D images when there is significant camera movement to facilitate motion parallax and when scene objects remain relatively static. However, in…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
This study addresses the challenge of simulating realistic particle systems by proposing a novel particle decomposition scheme that improves the parallel performance of surface resolved particle simulations. Realistic particle systems often…
In this paper, we study the Boltzmann equation with uncertainties and prove that the spectral convergence of the semi-discretized numerical system holds in a combined velocity and random space, where the Fourier-spectral method is applied…
Quantum computing holds great promise to accelerate scientific computations in fluid dynamics and other classical physical systems. While various quantum algorithms have been proposed for linear flows, developing quantum algorithms for…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
In this paper we present a numerical approach to solve the Navier-Stokes equations on moving domains with second-order accuracy. The space discretization is based on the ghost-point method, which falls under the category of unfitted…
Multi-objective optimization involving Quadratic Unconstrained Binary Optimization (QUBO) problems arises in various domains. A fundamental challenge in this context is the effective balancing of multiple objectives, each potentially…
We introduce a filtering technique for Discontinuous Galerkin approximations of hyperbolic problems. Following an approach already proposed for the Hamilton-Jacobi equations by other authors, we aim at reducing the spurious oscillations…
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…
The present article investigates the convergence of a class of space-time discretization schemes for the Cauchy problem for linear parabolic stochastic partial differential equations (SPDEs) defined on the whole space. Sufficient conditions…
A novel hybrid computational method based on the discrete-velocity (DV) approximation, including the lattice-Boltzmann (LB) technique, is proposed. Numerical schemes for the kinetic equations are used in regions of rarefied flows, and LB…
We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include…
We present a space-time multiscale method for a parabolic model problem with an underlying coefficient that may be highly oscillatory with respect to both the spatial and the temporal variables. The method is based on the framework of the…
We discuss an efficient implementation of the iterative proportional scaling procedure in the multivariate Gaussian graphical models. We show that the computational cost can be reduced by localization of the update procedure in each…