Partitioned finite element method for structured discretization with mixed boundary conditions
Andrea Brugnoli, Flávio Luiz Cardoso-Ribeiro, Ghislain Haine, Paul Kotyczka
Abstract
The propagation of acoustic waves in a 2D geometrical domain under mixed boundary control is here described by means of the port-Hamiltonian (pH) formalism. A finite element based method is employed to obtain a consistently discretized model. To construct a model with mixed boundary control, two different methodologies are detailed: one employs Lagrange multipliers, the other relies on a virtual domain decomposition to interconnect models with different causalities. The two approaches are assessed numerically, by comparing the Hamiltonian and the state variables norm for progressively refined meshes.
Topics & Concepts
DiscretizationDomain decomposition methodsFinite element methodLagrange multiplierPolygon meshBoundary knot methodMathematicsBoundary value problemHamiltonian (control theory)Applied mathematicsMathematical analysisComputer scienceBoundary element methodGeometryMathematical optimizationStructural engineeringEngineeringControl and Stability of Dynamical SystemsAdvanced Numerical Methods in Computational MathematicsNumerical methods for differential equations