Generalized HPC method for the Poisson equation

Bardazzi, Andrea; Lugni, Claudio; Antuono, Matteo; Graziani, G.; Faltinsen, Odd M.

doi:10.1016/j.jcp.2015.07.026

Cited by 20 publications

(24 citation statements)

References 11 publications

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“…The study for the properties of 3D HPC methods is currently in progress as a further study. Moreover, the analysis regarding accuracy in Sections 2.2 and 3 can also be extended to the HPC‐based Poisson solver in Bardazzi et al, and calculations have already shown that the original solver can be further improved. This work will be included in a future publication.…”

Section: Conclusion and Future Studiesmentioning

confidence: 99%

“…In the remainder of the domain, where the Laplace equation applies, the more efficient HPC method could be used. Other studies that apply DD to couple different computational regions can be found in, eg, Colicchio and Greco Recently, Bardazzi et al generalized the original HPC method to solve the Poisson equation. In their paper, problems involving forcing terms with a strong singularity are solved successfully.…”

Section: Introductionmentioning

confidence: 99%

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Local and global properties of the harmonic polynomial cell method: In‐depth analysis in two dimensions

Hanssen

Siddiqui

et al. 2017

Numerical Meth Engineering

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A detailed and systematic analysis is performed on the local and global properties of the recently developed Harmonic Polynomial Cell (HPC) method, a very accurate and efficient field solver for problems governed by the Laplace equation. At the local cell level, a simple rule is identified for the proper choice of harmonic polynomials in the local representation of the velocity potential in cells with symmetry properties. The local solution error, its convergence rate, its dependence on the cell topology, its distribution inside the cell and its features across cells with different dimensions, are carefully examined with relevant findings for HPC numerical implementations. At the global level, the error convergence rate is analytically estimated in terms of error contributions from the boundary conditions and from inside the liquid domain. In most cases, the error associated with boundary conditions dominates the global error. In order to minimize it, Quadtree grid strategies or high-order local expressions of the velocity potential are proposed for cells near critical boundary portions. To model accurately the boundary conditions on rigid or deformable surfaces with generic geometries, three different grid strategies are proposed by adopting concepts of immersed boundary method and overlapping grids. They are comparatively studied for a circular rigid cylinder in infinite fluid and for the propagation of a free-surface wave. Then, an immersed boundary strategy, using numerical choices suggested in this paper, is successfully compared against a fully nonlinear Boundary Element Method for the case of a surface-piercing circular cylinder heaving in otherwise calm water.

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Section: Conclusion and Future Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Local and global properties of the harmonic polynomial cell method: In‐depth analysis in two dimensions

Hanssen

Siddiqui

et al. 2017

Numerical Meth Engineering

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“…with scalar-to-vector variable operator ς k T defined by (13) and adjoint boundary residual operator r˚, k BT defined by (19). Additionally, it holds…”

Section: Reformulation Of the Stabilization Bilinear Formmentioning

confidence: 99%

“…Several classical methods have been used to numerically solve problem (1) or variations thereof in the context of computational electromagnetism. A (by far) non-exhaustive list includes, in particular, [13,14,15,16,4,17,18] and the high-order method of [19]. Such methods are limited to standard element shapes and, in most cases, do not support nonconforming mesh refinement.…”

Section: Introductionmentioning

confidence: 99%

An a posteriori-driven adaptive Mixed High-Order method with application to electrostatics

Pietro

Specogna

2016

Journal of Computational Physics

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In this work we propose an adaptive version of the recently introduced Mixed High-Order method and showcase its performance on a comprehensive set of academic and industrial problems in computational electromagnetism. The latter include, in particular, the numerical modeling of comb-drive and MEMS devices. Mesh adaptation is driven by newly derived, residual-based error estimators. The resulting method has several advantageous features: It supports fairly general meshes, it enables arbitrary approximation orders, and has a moderate computational cost thanks to hybridization and static condensation. The a posteriori-driven mesh refinement is shown to significantly enhance the performance on problems featuring singular solutions, allowing to fully exploit the high-order of approximation.

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“…The application of high-order polynomials and the resultant sparse coefficient matrix indicate that the HPC method is time efficient and of high accuracy. Subsequent work and improvements were conducted in recent years [27][28][29][30] to circumvent more challenging problems. In contrast to the boundary element method (BEM), which is widely applied in potential flow computation, the HPC method is more time efficient and the computational cost is roughly proportional to the number of unknowns.…”

Section: Introductionmentioning

confidence: 99%

Liquid sloshing in an upright circular tank under periodic and transient excitations

et al. 2020

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Generalized HPC method for the Poisson equation

Cited by 20 publications

References 11 publications

Local and global properties of the harmonic polynomial cell method: In‐depth analysis in two dimensions

Local and global properties of the harmonic polynomial cell method: In‐depth analysis in two dimensions

An a posteriori-driven adaptive Mixed High-Order method with application to electrostatics

Liquid sloshing in an upright circular tank under periodic and transient excitations

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