Related papers: Existence results on Lagrange multiplier approach …
Recent works in deep learning have shown that integrating differentiable physics simulators into the training process can greatly improve the quality of results. Although this combination represents a more complex optimization task than…
Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder-Mead, Quasi-Newton, and Global) are investigated in conjunction with energy minimization principle to resolve the pressure and…
We study a Lagrangian numerical scheme for solution of a nonlinear drift diffusion equation on an interval. The discretization is based on the equation's gradient flow structure with respect to the Wasserstein distance. The scheme inherits…
Optimization is a major part of human effort. While being mathematical, optimization is also built into physics. For example, physics has the principle of Least Action, the principle of Minimum Entropy Generation, and the Variational…
In this work, using a unified framework consisting of third-order accurate discontinuous Galerkin schemes, we perform a comparison between five different numerical approaches to the free-surface shallow flow simulation on bottom steps.…
This article concerns the problem of computing solutions to state-constrained optimal control problems whose trajectory is affected by a flow field. This general mathematical framework is particularly pertinent to the requirements…
We study evolution equations on metric graphs with reservoirs, that is graphs where a one-dimensional interval is associated to each edge and, in addition, the vertices are able to store and exchange mass with these intervals. Focusing on…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
Discrete gradient methods are well-known methods of Geometric Numerical Integration, which preserve the dissipation of gradient systems. The preservation of the dissipation of a system is an important feature in numerous image processing…
A model to explain the statistics of the velocity gradients in the dissipation range of a turbulent flow is presented. The experimentally observed non-gaussian statistics is theoretically predicted by means of a thermodynamical analogy…
In this paper, we continue to study the fractional harmonic gradient flow on $S^{n-1}$ taking values in a general closed manifold $N \subset \mathbb{R}^n$, addressing global existence and uniqueness of solutions of energy class with…
We develop the theory of fractional gradient flows: an evolution aimed at the minimization of a convex, l.s.c.~energy, with memory effects. This memory is characterized by the fact that the negative of the (sub)gradient of the energy equals…
Strain-gradient theories of plasticity have been successful in modeling the behavior of complex materials. However, the traditional formulation of these theories lacks a material length scale, and is thus incapable of capturing…
This paper presents a gradient-based reconstruction approach for simulations of compressible single and multi-species Navier-Stokes equations. The novel feature of the proposed algorithm is the efficient reconstruction via derivative…
We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its…
We study the stochastic total variation flow (STVF) equation with linear multiplicative noise. By considering a limit of a sequence of regularized stochastic gradient flows with respect to a regularization parameter $\varepsilon$ we obtain…
In this article, we discuss gradient robust discretizations for the simulation of non-linear incompressible Navier-Stokes problem and the optimal control of such flow. We consider several formulations of the flow problem that are equivalent…
This paper investigates the privacy-preserving distributed optimization problem, aiming to protect agents' private information from potential attackers during the optimization process. Gradient tracking, an advanced technique for improving…
In this paper, new unfitted mixed finite elements are presented for elliptic interface problems with jump coefficients. Our model is based on a fictitious domain formulation with distributed Lagrange multiplier. The relevance of our…
We extend the divergence preserving cut finite element method presented in [T. Frachon, P. Hansbo, E. Nilsson, S. Zahedi, SIAM J. Sci. Comput., 46 (2024)] for the Darcy interface problem to unfitted outer boundaries. We impose essential…