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Branch-and-Bound (B&B) algorithms are time intensive tree-based exploration methods for solving to optimality combinatorial optimization problems. In this paper, we investigate the use of GPU computing as a major complementary way to speed…
First-order optimization methods, such as stochastic gradient descent (SGD) and its variants, are widely used in machine learning applications due to their simplicity and low per-iteration costs. However, they often require larger numbers…
Differentiable simulation of soft bodies is a foundation for system identification, trajectory optimization, and Real2Sim transfer. Yet, existing methods such as the differentiable Projective Dynamics (DiffPD) struggle when faced with…
The paper proposes an approach for the efficient model order reduction of dynamic contact problems in linear elasticity. Instead of the augmented Lagrangian method that is widely used for mechanical contact problems, we prefer here the…
A numerical method for simulation of bubble dynamics in three-dimensional potential flows is presented. The approach is based on the boundary element method for the Laplace equation accelerated via the fast multipole method implemented on a…
We investigate the potential of Graphics Processing Units (GPUs) to solve large-scale nonlinear programs with a dynamic structure. Using ExaModels, a GPU-accelerated automatic differentiation tool, and the interior-point solver MadNLP, we…
This paper proposes and analyzes a proximal augmented Lagrangian (NL-IAPIAL) method for solving smooth nonconvex composite optimization problems with nonlinear $\cal K$-convex constraints, i.e., the constraints are convex with respect to…
An efficient solver for the three dimensional free-space Poisson equation is presented. The underlying numerical method is based on finite Fourier series approximation. While the error of all involved approximations can be fully controlled,…
This paper introduces a sharp interface method to simulate fluid-structure interaction (FSI) involving rigid bodies immersed in viscous incompressible fluids. The capabilities of this methodology are demonstrated for a range of benchmark…
The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or…
Current supercomputers often have a heterogeneous architecture using both CPUs and GPUs. At the same time, numerical simulation tasks frequently involve multiphysics scenarios whose components run on different hardware due to multiple…
The immersed boundary (IB) method is a mathematical and numerical framework for problems of fluid-structure interaction, treating the particular case in which an elastic structure is immersed in a viscous incompressible fluid. The IB…
Finding the stationary states of a free energy functional is an important problem in phase field crystal (PFC) models. Many efforts have been devoted for designing numerical schemes with energy dissipation and mass conservation properties.…
The present work describes the development of heterogeneous GPGPU implicit CFD coupled solvers, encompassing both density- and pressure- based approaches. In this setup, the assembled linear matrix is offloaded onto multiple GPUs using…
Motivated by variational models in continuum mechanics, we introduce a novel algorithm to perform nonsmooth and nonconvex minimizations with linear constraints in Euclidean spaces. We show how this algorithm is actually a natural…
We present a framework for the simulation of rigid and deformable bodies in the presence of contact and friction. Our method is based on a non-smooth Newton iteration that solves the underlying nonlinear complementarity problems (NCPs)…
In the subsurface, fractures and the surrounding porous rock can deform in interaction with fluid flow. Advanced mathematical models governing these coupled processes typically combine fluid flow, poroelasticity, and fracture contact…
In this paper, we consider a class of convex programming problems with linear equality constraints, which finds broad applications in machine learning and signal processing. We propose a new adaptive balanced augmented Lagrangian (ABAL)…
This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…
We present the barycentric Lagrange dual tree traversal (BLDTT) fast summation method for particle interactions. The scheme replaces well-separated particle-particle interactions by adaptively chosen particle-cluster, cluster-particle, and…