2018
DOI: 10.1016/j.jcp.2018.06.051
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Finite differences on staggered grids preserving the port-Hamiltonian structure with application to an acoustic duct

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Cited by 45 publications
(24 citation statements)
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References 28 publications
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“…In this particular case, the constitutive relations needed for system (10) to be well-defined are given by (15), and then directly included in (18). In Sections 3.2 and 3.3, it will be shown that PFEM leads directly to a finite-dimensional pHs of the form (1) with…”
Section: Hyperbolic Systemsmentioning
confidence: 99%
See 1 more Smart Citation
“…In this particular case, the constitutive relations needed for system (10) to be well-defined are given by (15), and then directly included in (18). In Sections 3.2 and 3.3, it will be shown that PFEM leads directly to a finite-dimensional pHs of the form (1) with…”
Section: Hyperbolic Systemsmentioning
confidence: 99%
“…Unfortunately, this method seems to be limited to the one-dimensional case. A finite difference method with staggered grids was developed in [15] for two-dimensional domains, but complex geometries are then difficult to tackle. Weak formulations leading to Galerkin numerical approximations began to be explored in the past few years.…”
Section: Introductionmentioning
confidence: 99%
“…The discritization method used in this paper is the mixed finite element method used to preserve the port-Hamiltonian structure such that we can use passivity-based control using the discretized finite dimensional system (15). We can also use other structure-preserving methods to discretize the system (12), such as the pseudo-spectral method [22], the finite difference method on a staggered grid [23], and the finite volume structure-preserving discretization method [24].…”
Section: The Ipmc Actuator Modelmentioning
confidence: 99%
“…Formally,the control design concerns the solution of PDEs, leading to the study of existence and decay of classical solutions of hyperbolic systems, using for instance a Riemann invariants approach [18], [19] or operator theory [20]. Alternatives to control design approaches based on models described by PDEs are early lumping approaches [21], in which the PDEs are spatially approximated by a set of ordinary differential equations (ODEs). The advantage of working with ODEs is that simpler control design techniques can be used although at the expense of possibly losing the physical interpretation of the model and the parameters.…”
Section: Symbolmentioning
confidence: 99%