Related papers: High-performance computing for the BGK model of th…
This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…
As a sequel to our previous work [C. Ma, Q. Zhang and W. Zheng, SIAM J. Numer. Anal., 60 (2022)], [C. Ma and W. Zheng, J. Comput. Phys. 469 (2022)], this paper presents a generic framework of arbitrary Lagrangian-Eulerian unfitted finite…
For the purposes of electric circuit simulation, we consider an iterative simulation model based on solving systems of linear equations by Gauss-Jordan elimination (GJE) for individual moments in time. To accelerate the simulation, we…
We present an ``equation-free'' multiscale approach to the simulation of unsteady diffusion in a random medium. The diffusivity of the medium is modeled as a random field with short correlation length, and the governing equations are cast…
Despite the development of an extensive toolbox of multi-scale rarefied flow simulators, such simulations remain challenging due to the significant disparity of collisional and macroscopic spatio-temporal scales. Our study offers a novel…
A virtual element discretisation of an Arbitrary Lagrangian-Eulerian method for two-dimensional convection-diffusion equations is proposed employing an isoparametric Virtual Element Method to achieve higher-order convergence rates on curved…
Two discretizations of a 9-velocity Boltzmann equation with a BGK collision operator are studied. A Chapman-Enskog expansion of the PDE system predicts that the macroscopic behavior corresponds to the incompressible Navier-Stokes equations…
Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of…
Building surrogate models is one common approach when we attempt to learn unknown black-box functions. Bayesian optimization provides a framework which allows us to build surrogate models based on sequential samples drawn from the function…
With recent advances in variable-length structures for use in soft actuation, energy harvesting, energy dissipation and metamaterials, the mathematical modelling and numerical simulation of physical systems with time-varying domains is…
In this paper, we propose and analyze an accelerated linearized Bregman (ALB) method for solving the basis pursuit and related sparse optimization problems. This accelerated algorithm is based on the fact that the linearized Bregman (LB)…
We propose a GPU-based iterative method for accelerated elastodynamic simulation with the log-barrier-based contact model. While Newton's method is a conventional choice for solving the interior-point system, the presence of ill-conditioned…
High-fidelity complex engineering simulations are highly predictive, but also computationally expensive and often require substantial computational efforts. The mitigation of computational burden is usually enabled through parallelism in…
This contribution investigates the connection between isogeometric analysis and integral equation methods for full-wave electromagnetic problems up to the low-frequency limit. The proposed spline-based integral equation method allows for an…
Kernel methods for solving partial differential equations on surfaces have the advantage that those methods work intrinsically on the surface and yield high approximation rates if the solution to the partial differential equation is smooth…
The Poisson-Fermi model is an extension of the classical Poisson-Boltzmann model to include the steric and correlation effects of ions and water treated as nonuniform spheres in aqueous solutions. Poisson-Boltzmann electrostatic…
The goal of this paper is to study a multi-objective linear quadratic Gaussian (LQG) control problem. In particular, we consider an optimal control problem minimizing a quadratic cost over a finite time horizon for linear stochastic systems…
Large language models (LLMs) have been widely applied but face challenges in efficient inference. While quantization methods reduce computational demands, ultra-low bit quantization with arbitrary precision is hindered by limited GPU Tensor…
Approximate Bayesian computation (ABC) methods are used to approximate posterior distributions using simulation rather than likelihood calculations. We introduce Gaussian process (GP) accelerated ABC, which we show can significantly reduce…
Scalable surrogate models enable efficient emulation of computer models (or simulators), particularly when dealing with large ensembles of runs. While Gaussian process (GP) models are commonly employed for emulation, they face limitations…