Related papers: Simulation-Driven Optimization of High-Order Meshe…
In recent years, there has been a growing interest in understanding complex microstructures and their effect on macroscopic properties. In general, it is difficult to derive an effective constitutive law for such microstructures with…
Building efficient, accurate and generalizable reduced order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for…
Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this…
This study introduces a first step for constructing a hybrid reduced-order models (ROMs) for segregated fluid-structure interaction in an Arbitrary Lagrangian-Eulerian (ALE) approach at a high Reynolds number using the Finite Volume Method…
We present a high-order method for flow simulation on unstructured curved nonconforming sliding meshes. This method utilizes dynamic transfinite mortar elements to exchange flow information between the two sides of a sliding interface. The…
We present a new family of very high order accurate direct Arbitrary-Lagrangian-Eulerian (ALE) Finite Volume (FV) and Discontinuous Galerkin (DG) schemes for the solution of nonlinear hyperbolic PDE systems on moving 2D Voronoi meshes that…
The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is…
We propose a novel Model Order Reduction framework that is able to handle solutions of hyperbolic problems characterized by multiple travelling discontinuities. By means of an optimization based approach, we introduce suitable calibration…
We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real-time using higher-order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this…
We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatible with higher-order finite element discretizations of…
We devise and evaluate numerically a Hybrid High-Order (HHO) method for finite plasticity within a logarithmic strain framework. The HHO method uses as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together…
We derive several numerical methods for designing optimized first-order algorithms in unconstrained convex optimization settings. Our methods are based on the Performance Estimation Problem (PEP) framework, which casts the worst-case…
We present a novel second-order semi-implicit hybrid finite volume / finite element (FV/FE) scheme for the numerical solution of the incompressible and weakly compressible Navier-Stokes equations on moving unstructured meshes using an…
The complicated mesoscopic configurations of composite plate and shell structures requires a huge amount of computational overhead for directly simulating their mechanical problems. In this paper, a unified high-order multi-scale method,…
An approach to derive low-complexity models describing thermal radiation for the sake of simulating the behavior of electric arcs in switchgear systems is presented. The idea is to approximate the (high dimensional) full-order equations,…
Mesh-free methods have significant potential for simulations of flows in complex geometries, with the difficulties of domain discretisation greatly reduced. However, many mesh-free methods are limited to low order accuracy. In order to…
In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial…
An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…