Related papers: Algebraic Multigrid with Filtering: An Efficient P…
Many techniques for real-time trajectory optimization and control require the solution of optimization problems at high frequencies. However, ill-conditioning in the optimization problem can significantly reduce the speed of first-order…
Functionally Graded Materials (FGMs) made of soft constituents have emerged as promising material-structure systems in potential applications across many engineering disciplines, such as soft robots, actuators, energy harvesting, and tissue…
We investigate the performance of multigrid preconditioners for solving linear systems arising from finite element discretizations of elliptic interface problems using the Fictitious Domain with Distributed Lagrange Multipliers (FD-DLM)…
In this paper, we propose a meshfree approximation method for the implicit filter developed in [2], which is a novel numerical algorithm for nonlinear filtering problems. The implicit filter approximates conditional distributions in the…
A novel Material Point Method (MPM) is introduced for addressing frictional contact problems. In contrast to the standard multi-velocity field approach, this method employs a penalty method to evaluate contact forces at the discretised…
Recent advances in the field of machine learning open a new era in high performance computing. Applications of machine learning algorithms for the development of accurate and cost-efficient surrogates of complex problems have already…
The aim of this paper is to solve linear semidefinite programs arising from higher-order Lasserre relaxations of unconstrained binary quadratic optimization problems. For this we use an interior point method with a preconditioned conjugate…
We solve large-scale mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This is motivated by the MILPs being able to model problems in multi-agent autonomy, e.g., task assignment problems and…
In this paper, we develop an efficient preconditioned unfitted finite element method for the elliptic interface problem, based on the reconstructed discontinuous approximation. The approximation method for interface problems is originally…
Challenging aspects of large-scale turbulent edge simulations in plasma physics include robust nonlinear solvers and efficient preconditioners. This paper presents recent advances in the scalable solution of nonlinear partial differential…
Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…
Large Language Model (LLM) based multi-agent systems have shown remarkable performance in various tasks, especially when enhanced through collaborative communication. However, current methods often rely on a fixed number of agents and…
In contact mechanics computation, the constraint conditions on the contact surfaces are typically enforced by the Lagrange multiplier method, resulting in a saddle point system. Given that the saddle point matrix is indefinite, solving…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
Our current understanding of the structure and dynamics of aqueous interfaces at the molecular level has grown substantially in the last few decades due to the continuous development of surface-specific spectroscopies, such as vibrational…
An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents…
Fully realizing the potential of multigrid solvers often requires custom algorithms for a given application model, discretizations and even regimes of interest, despite considerable effort from the applied math community to develop fully…
This paper develops a new algebraic multigrid (AMG) method for sparse least-squares systems of the form $A=G^TG$ motivated by challenging applications in scientific computing where classical AMG methods fail. First we review and relate the…
We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth…
Most linear algebra kernels in interior point methods for linear programming require the solution of linear systems of equation with the matrix $N = A^TD^{-1}A$ (or $AD^{-1}A^T$), where $A$ denotes the constraint matrix of the linear…