Related papers: An Efficient Coarse Grid Projection Method for Qua…

A parallel dynamic overset framework has been developed for the curvilinear immersed boundary (overset-CURVIB) method to enable tackling a wide range of challenging flow problems. The dynamic overset grids are used to locally increase the…

We present a method to simulate nonhydrostatic ocean flows on a horizontally-unstructured grid with a moving generalized vertical coordinate (GVC). The nonhydrostatic governing equations are transformed to a GVC system that can represent…

We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In…

Potential flow has many applications, including the modelling of unsteady flows in aerodynamics. For these models to work efficiently, it is best to avoid Biot-Savart interactions. This work presents a grid-based treatment of potential…

This paper is to give an overview of AMG methods for solving large scale systems of equations such as those from the discretization of partial differential equations. AMG is often understood as the acronym of "Algebraic Multi-Grid", but it…

Partitioning for load balancing is a crucial first step to parallelize any type of computation. In this work, we propose SGORP, a new spatial partitioning method based on Subgradient Optimization, to solve the $d$-dimensional Rectilinear…

Modern GPUs are equipped with large amounts of high-bandwidth memory, enabling them to support mini-batch sizes of up to tens of thousands of training samples. However, most existing optimizers struggle to perform effectively at such a…

High dimensional unconstrained quadratic programs (UQPs) involving massive datasets are now common in application areas such as web, social networks, etc. Unless computational resources that match up to these datasets are available, solving…

This paper introduces cuHALLaR, a GPU-accelerated implementation of the HALLaR method proposed in Monteiro et al. 2024 for solving large-scale semidefinite programming (SDP) problems. We demonstrate how our Julia-based implementation…

Inverse problems span across diverse fields. In medical contexts, computed tomography (CT) plays a crucial role in reconstructing a patient's internal structure, presenting challenges due to artifacts caused by inherently ill-posed inverse…

Robot programming tools ranging from inverse kinematics (IK) to model predictive control (MPC) are most often described as constrained optimization problems. Even though there are currently many commercially-available second-order solvers,…

We propose a data-driven framework for efficiently solving quadratic programming (QP) problems by reducing the number of variables in high-dimensional QPs using instance-specific projection. A graph neural network-based model is designed to…

Graph Convolutional Network (GCN) is a model that can effectively handle graph data tasks and has been successfully applied. However, for large-scale graph datasets, GCN still faces the challenge of high computational overhead, especially…

We propose an efficient reconstruction algorithm named the frozen Gaussian grid-point correction (FGGC) for computing the Schr\"odinger equation in the semi-classical regime using the frozen Gaussian approximation (FGA). The FGA has…

The problem of Cortical Surface Reconstruction from magnetic resonance imaging has been traditionally addressed using lengthy pipelines of image processing techniques like FreeSurfer, CAT, or CIVET. These frameworks require very long…

We consider quasi-geostrophic (Q-G) models in two- and three-layers that are useful in theoretical studies of planetary atmospheres and oceans. In these models, the streamfunctions are given by (1+2) partial differen- tial systems of…

This article considers the extension of two-grid $hp$-version discontinuous Galerkin finite element methods for the numerical approximation of second-order quasilinear elliptic boundary value problems of monotone type to the case when…

Many iterative parallel-in-time algorithms have been shown to be highly efficient for diffusion-dominated partial differential equations (PDEs), but are inefficient or even divergent when applied to advection-dominated PDEs. We consider the…

This paper presents Space-Time MultiGrid (STMG) methods which are suitable for performing topology optimisation of transient heat conduction problems. The proposed methods use a pointwise smoother and uniform Cartesian space-time meshes.…

3D Gaussian Splatting (3DGS) achieves impressive rendering fidelity and speed for novel view synthesis. However, its substantial data size poses a significant challenge for practical applications. While many compression techniques have been…