Related papers: A-ULMPM: An Arbitrary Updated Lagrangian Material …
We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations, exploiting the inherent conservative structure to achieve stable long-range…
In this paper, we propose a stabilised finite element method for the numerical solution of contact between a small deformation elastic membrane and a rigid obstacle. We limit ourselves to friction--free contact, but the formulation is…
Necessary optimality conditions in Lagrangian form and the sequential minimization framework are extended to mixed-integer nonlinear optimization, without any convexity assumptions. Building upon a recently developed notion of local…
Accurately handling contact with friction remains a core bottleneck for Material Point Method (MPM), from reliable contact point detection to enforcing frictional contact laws (non-penetration, Coulomb friction, and maximum dissipation…
The Lagrangian theory of structure formation in cosmological fluids, restricted to the matter model ``dust'', provides successful models of large-scale structure in the Universe in the laminar regime, i.e., where the fluid flow is…
Euler's elastica model has been extensively studied and applied to image processing tasks. However, due to the high nonlinearity and nonconvexity of the involved curvature term, conventional algorithms suffer from slow convergence and high…
The objective of this paper is to introduce and demonstrate a robust method for multi-constrained topology optimization. The method is derived by combining the topological sensitivity with the classic augmented Lagrangian formulation. The…
We present a Lagrangian-Eulerian scheme to solve the shallow water equations in the case of spatially variable bottom geometry. Using a local curvilinear reference system anchored on the bottom surface, we develop an effective first-order…
Compressible Mooney-Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of soft tissues for biomedical tissues, undergoing large elastic deformations. We propose a…
Universal Machine Learning Interactomic Potentials (MLIPs) enable accelerated simulations for materials discovery. However, current research efforts fail to impactfully utilize MLIPs due to: 1. Overreliance on Density Functional Theory…
We present a localized a-posteriori error estimate for the localized reduced basis multi-scale (LRBMS) method [Albrecht, Haasdonk, Kaulmann, Ohlberger (2012): The localized reduced basis multiscale method]. The LRBMS is a combination of…
This study presents a novel approach to applying data assimilation techniques for particle-based simulations using the Ensemble Kalman Filter. While data assimilation methods have been effectively applied to Eulerian simulations, their…
We investigate the purely spatial Lagrangian coordinate transformation from the Lagrangian to the basic Eulerian frame. We demonstrate three techniques for extracting the relativistic displacement field from a given solution in the…
A new algorithm is introduced to integrate the equations of rotational motion. The algorithm is derived within a leapfrog framework and the quantities involved into the integration are mid-step angular momenta and on-step orientational…
Smooth-Particle-Hydrodynamics is gaining popularity for the simulation of solids subjected to machining, wear, and impacts. Its attractiveness is due to its abilities to simulate problems involving large deformations resulting from the…
The Augmented Lagragian Method (ALM) and Alternating Direction Method of Multiplier (ADMM) have been powerful optimization methods for general convex programming subject to linear constraint. We consider the convex problem whose objective…
Lagrangian algorithms to simulate the evolution of cold dark matter (CDM) are invaluable tools to generate large suites of mock halo catalogues. In this paper, we first show that the main limitation of current semi-analytical schemes to…
We present an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. Local, third-order, least-squares, polynomial…
Learning-based methods have made significant progress in physics simulation, typically approximating dynamics with a monolithic end-to-end optimized neural network. Although these models offer an effective way to simulation, they may lose…
This paper presents two new techniques relating to inexact solution of subproblems in augmented Lagrangian methods for convex programming. The first involves combining a relative error criterion for solution of the subproblems with over- or…