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We introduce a fast direct solver for variable-coefficient elliptic partial differential equations on surfaces based on the hierarchical Poincar\'e-Steklov method. The method takes as input an unstructured, high-order quadrilateral mesh of…
3D Gaussian Splatting (3DGS) has revolutionized radiance field reconstruction by achieving high-quality novel view synthesis with fast rendering speed, introducing 3D Gaussian primitives to represent the scene. However, 3DGS encounters…
Research on smooth vector graphics is separated into two independent research threads: one on interpolation-based gradient meshes and the other on diffusion-based curve formulations. With this paper, we propose a mathematical formulation…
We propose a CPU-GPU heterogeneous computing method for solving time-evolution partial differential equation problems many times with guaranteed accuracy, in short time-to-solution and low energy-to-solution. On a single-GH200 node, the…
Monte Carlo Localization is a widely used approach in the field of mobile robotics. While this problem has been well studied in the 2D case, global localization in 3D maps with six degrees of freedom has so far been too computationally…
Extensions to the C++ implementation of the QCD Data Parallel Interface are provided enabling acceleration of expression evaluation on NVIDIA GPUs. Single expressions are off-loaded to the device memory and execution domain leveraging the…
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…
Detailed analysis of efficiency and pollutant emission characteristics of practical turbulent combustion devices using complex combustion kinetics often depend on the interactions between the combustion chemistry involving both gasses…
Different hybrid quantum-classical algorithms have recently been developed as a near-term way to solve linear systems of equations on quantum devices. However, the focus has so far been mostly on the methods, rather than the problems that…
Running kinetic simulations using grid-based methods is extremely expensive due to the up to six-dimensional phase space. Recently, it has been shown that dynamical low-rank algorithms can drastically reduce the required computational…
Recently, a nonlinear Poisson equation has been introduced to model nonlinear and nonlocal hyperpolarization effects in electrostatic solute-solvent interaction for biomolecular solvation analysis. Due to a strong nonlinearity associated…
This paper develops a robust solver for the Maxwell eigenproblem in 3D photonic crystals with anisotropic media. The solver employs the kernel compensation technique under the framework of Yee's scheme to eliminate null space and enable…
A novel and scalable geometric multi-level algorithm is presented for the numerical solution of elliptic partial differential equations, specially designed to run with high occupancy of streaming processors inside Graphics Processing…
This paper describes the main features of a pioneering unsteady solver for simulating ideal two-fluid plasmas on unstructured grids, taking profit of GPGPU (General-purpose computing on graphics processing units). The code, which has been…
In this paper, the discontinuous Galerkin based high-order gas-kinetic schemes (DG-HGKS) are developed for the three-dimensional Euler and Navier-Stokes equations. Different from the traditional discontinuous Galerkin (DG) methods with…
The radiative transport equation accurately describes light transport in participating media such as biological tissues, though analytic solutions are known only for simple geometries. We present a pseudospectral technique to efficiently…
Many problems in geophysical and atmospheric modelling require the fast solution of elliptic partial differential equations (PDEs) in "flat" three dimensional geometries. In particular, an anisotropic elliptic PDE for the pressure…
We propose in this paper a Proper Generalized Decomposition (PGD) solver for reduced-order modeling of linear elastodynamic problems. It primarily focuses on enhancing the computational efficiency of a previously introduced PGD solver based…
We present a new and very fast method for producing microlensing magnification maps at high optical depths. It is based on the combination of two approaches: (a) the two-dimensional Poisson solver for a deflection potential and (b) inverse…
[Abridged] We present the results of a highly parallel Kepler equation solver using the Graphics Processing Unit (GPU) on a commercial nVidia GeForce 280GTX and the "Compute Unified Device Architecture" programming environment. We apply…