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The problem of finding dense components of a graph is a widely explored area in data analysis, with diverse applications in fields and branches of study including community mining, spam detection, computer security and bioinformatics. This…

We discuss an approach for solving sparse or dense banded linear systems ${\bf A} {\bf x} = {\bf b}$ on a Graphics Processing Unit (GPU) card. The matrix ${\bf A} \in {\mathbb{R}}^{N \times N}$ is possibly nonsymmetric and moderately large;…

Diffusion models have achieved great success in synthesizing high-quality images. However, generating high-resolution images with diffusion models is still challenging due to the enormous computational costs, resulting in a prohibitive…

As the need for computational power and efficiency rises, parallel systems become increasingly popular among various scientific fields. While multiple core-based architectures have been the center of attention for many years, the rapid…

Simultaneous matrix diagonalization is used as a subroutine in many machine learning problems, including blind source separation and paramater estimation in latent variable models. Here, we extend algorithms for performing joint…

This paper first proposes an N-block PCPM algorithm to solve N-block convex optimization problems with both linear and nonlinear constraints, with global convergence established. A linear convergence rate under the strong second-order…

Chan-Vese algorithms have proven to be a first-class method for image segmentation. Early implementations used level set methods with a pixelwise representation of the level set function. Later, parametrized level set approximations, such…

Efficient large-scale inference of transformer-based large language models (LLMs) remains a fundamental systems challenge, frequently requiring multi-GPU parallelism to meet stringent latency and throughput targets. Conventional tensor…

To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a…

Here a semi-implicit formulation of the gradient augmented level set method is presented. By tracking both the level set and it's gradient accurate subgrid information is provided,leading to highly accurate descriptions of a moving…

The prediction of a dielectric breakdown in a high-voltage device is based on criteria that evaluate the electric field along field lines. Therefore it is necessary to efficiently compute the electric field at arbitrary points in space. A…

We explore a new way to handle flux boundary conditions imposed on level sets. The proposed approach is a diffuse interface version of the shifted boundary method (SBM) for continuous Galerkin discretizations of conservation laws in…

Developing an efficient server-based real-time scheduling solution that supports dynamic task-level parallelism is now relevant to even the desktop and embedded domains and no longer only to the high performance computing market niche. This…

Parametric linear programming is a central operation for polyhedral computations, as well as in certain control applications.Here we propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.This type…

Obtaining high quality particle distribution representing clean geometry in pre-processing is essential for the simulation accuracy of the particle-based methods. In this paper, several level-set based techniques for cleaning up `dirty'…

Processing large complex networks like social networks or web graphs has recently attracted considerable interest. In order to do this in parallel, we need to partition them into pieces of about equal size. Unfortunately, previous parallel…

The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for…

A new higher-order accurate method is proposed that combines the advantages of the classical $p$-version of the FEM on body-fitted meshes with embedded domain methods. A background mesh composed by higher-order Lagrange elements is used.…

We propose a deep learning strategy to estimate the mean curvature of two-dimensional implicit interfaces in the level-set method. Our approach is based on fitting feed-forward neural networks to synthetic data sets constructed from…

We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…