A structure-preserving Partitioned Finite Element Method for the 2D wave equation

被引：23

作者：

Cardoso-Ribeiro, Flavio Luiz ^{[1
]}

Matignon, Denis ^{[2
]}

Lefevre, Laurent ^{[3
]}

机构：

[1] Inst Tecnol Aeronaut, Sao Jose Dos Campos, Brazil

[2] Univ Toulouse, ISAE SUPAERO, Toulouse, France

[3] Univ Grenoble Alpes, LCIS, F-26902 Valence, France

来源：

IFAC PAPERSONLINE | 2018年 / 51卷 / 03期

关键词：

Distributed Parameter systems; Port-Hamiltonian systems; Finite Element Method; Geometric Discretization Methods; 2D Wave equation; DISCRETIZATION; SYSTEMS;

D O I：

10.1016/j.ifacol.2018.06.033

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Discretizing open systems of conservation laws while preserving the power-balance at the discrete level can be achieved using a new Partitioned Finite Element Method (PFEM), where an integration by parts is performed only on a subset of the variables in the weak formulation. Moreover, since boundary control and observation appear naturally in this formulation, the method is suitable both for simulation and control of infinite-dimensional port Hamiltonian systems. The method can be applied using FEM software, and comes along with worked-out test cases on the 2D wave equation in different geometries and coordinate systems. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

引用

页码：119 / 124

页数：6

共 17 条

[1]

Boyd JP, 2001, Chebyshev and Fourier spectral methods

[2]

Cardoso-Ribeiro F. L, 2018, PARTITIONED FI UNPUB

[3] Piezoelectric beam with distributed control ports: a power-preserving discretization using weak formulation. [J].

Cardoso-Ribeiro, Flavio Luiz ;

Matignon, Denis ;

Pommier-Budinger, Valerie .

IFAC PAPERSONLINE, 2016, 49 (08) :290-297

[4]

Duindam V, 2009, MODELING AND CONTROL OF COMPLEX PHYSICAL SYSTEMS: THE PORT-HAMILTONIAN APPROACH, P1, DOI 10.1007/978-3-642-03196-0

[5]

Farle O., 2013, 2013 International Conference on Electromagnetics in Advanced Applications (ICEAA), P324, DOI 10.1109/ICEAA.2013.6632246

[6]

Farle O, 2014, P 21 INT S MATH THEO, P724

[7] Structure-Preserving Discretization of Distributed-Parameter Port-Hamiltonian Systems Using Finite Elements [J].

Farle, Ortwin ;

Baltes, Rolf-Bjoern ;

Dyczij-Edlinger, Romanus .

AT-AUTOMATISIERUNGSTECHNIK, 2014, 62 (07) :500-511

[8] Hamiltonian discretization of boundary control systems [J].

Golo, G ;

Talasila, V ;

van der Schaft, A ;

Maschke, B .

AUTOMATICA, 2004, 40 (05) :757-771

[9] New development in freefem++ [J].

Hecht, F. .

JOURNAL OF NUMERICAL MATHEMATICS, 2012, 20 (3-4) :251-265

[10] High order geometric methods with exact conservation properties [J].

Hiemstra, R. R. ;

Toshniwal, D. ;

Huijsmans, R. H. M. ;

Gerritsma, M. I. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 257 :1444-1471

← 1 2 →