Related papers: A Structure-Preserving Domain Decomposition Method…
In this contribution, a finite element scheme to impose mixed boundary conditions without introducing Lagrange multipliers is presented for hyperbolic systems described as port-Hamiltonian systems. The strategy relies on finite element…
Methods for discretizing port-Hamiltonian systems are of interest both for simulation and control purposes. Despite the large literature on mixed finite elements, no rigorous analysis of the connections between mixed elements and…
We develop a density based topology optimization method for linear elasticity based on the cut finite element method. More precisely, the design domain is discretized using cut finite elements which allow complicated geometry to be…
We present domain decomposition finite element/finite difference method for the solution of hyperbolic equation. The domain decomposition is performed such that finite elements and finite differences are used in different subdomains of the…
This paper presents a structure-preserving spatial discretization method for distributed parameter port-Hamiltonian systems. The class of considered systems are hyperbolic systems of two conservation laws in arbitrary spatial dimension and…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…
This paper presents a new data-driven finite element framework that is applicable to a broad range of engineering simulation problems. In the data-driven approach, the conservation laws and boundary conditions are satisfied by means of the…
This paper contributes with a new formal method of spatial discretization of a class of nonlinear distributed parameter systems that allow a port-Hamiltonian representation over a one dimensional manifold. A specific finite dimensional…
Non-overlapping domain decomposition methods necessarily have to exchange Dirichlet and Neumann traces at interfaces in order to be able to converge to the underlying mono-domain solution. Well known such non-overlapping methods are the…
This paper presents some applications of using recently developed algorithms for smooth-continuous data reconstruction based on the digital-discrete method. The classical discrete method for data reconstruction is based on domain…
We construct a finite element discretization and time-stepping scheme for the incompressible Euler equations with variable density that exactly preserves total mass, total squared density, total energy, and pointwise incompressibility. The…
This paper presents some applications using recently developed algorithms for smooth-continuous data reconstruction based on the digital-discrete method. The classical discrete method for data reconstruction is based on domain decomposition…
This paper investigates the problem of data-driven modeling of port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability properties. We propose a novel neural-network-based port-Hamiltonian modeling…
Domain decomposition methods are used for approximate solving boundary problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are taken into account in the most complete way in…
A mass-conservative high-order unfitted finite element method for convection-diffusion equations in evolving domains is proposed. The space-time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307…
This article reports on the confluence of two streams of research, one emanating from the fields of numerical analysis and scientific computation, the other from topology and geometry. In it we consider the numerical discretization of…
We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradient flows, and certain systems with algebraic constraints. Our…
This paper is concerned with the finite element discretization of the data driven approach according to arXiv:1510.04232 for the solution of PDEs with a material law arising from measurement data. To simplify the setting, we focus on a…
In this contribution we develop a cut finite element method with boundary value correction of the type originally proposed by Bramble, Dupont, and Thomee. The cut finite element method is a fictitious domain method with Nitsche type…
We propose a linear finite-element discretization of Dirichlet problems for static Hamilton-Jacobi equations on unstructured triangulations. The discretization is based on simplified localized Dirichlet problems that are solved by a local…