A discontinuous‐Galerkin‐based immersed boundary method

Lew, Adrián J.; Buscaglia, Gustavo C.

doi:10.1002/nme.2312

Cited by 93 publications

(106 citation statements)

References 82 publications

(91 reference statements)

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“…When the complete variationl formulation (47) is discretized (see section 3.2), the internal work integrals (48) and (52) The matrix and vector coefficients of the discrete equations follow from the partial derivatives of equations (48) and (49) with respect to the displacement degrees of freedom in analogy to (44). In particular, the discretized form K N IT rs is computed as…”

Section: Discretization Aspectsmentioning

confidence: 99%

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A parameter-free variational coupling approach for trimmed isogeometric thin shells

2016

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The non-symmetric variant of Nitsche's method was recently applied successfully for variationally enforcing boundary and interface conditions in non-boundary-fitted discretizations. In contrast to its symmetric variant, it does not require stabilization terms and therefore does not depend on the appropriate estimation of stabilization parameters. In this paper, we further consolidate the non-symmetric Nitsche approach by establishing its application in isogeometric thin shell analysis, where variational coupling techniques are of particular interest for enforcing interface conditions along trimming curves. To this end, we extend its variational formulation within Kirchhoff-Love shell theory, combine it with the finite cell method, and apply the resulting framework to a range of representative shell problems based on trimmed NURBS surfaces. We demonstrate that the non-symmetric variant applied in this context is stable and can lead to the same accuracy in terms of displacements and stresses as its symmetric counterpart. Based on our numerical evidence, the non-symmetric Nitsche method is a viable parameter-free alternative to the symmetric variant in elastostatic shell analysis.

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Section: Discretization Aspectsmentioning

confidence: 99%

“…Moreover, accurate estimation techniques are often delicate from an algorithmic viewpoint [43,44,46]. Therefore, there has been an increasing interest in methods that can enforce boundary and interface conditions without mesh dependent stabilization parameters [38,[47][48][49].…”

Section: Introductionmentioning

confidence: 99%

A parameter-free variational coupling approach for trimmed isogeometric thin shells

2016

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“…Depending on the choice of interpolation in the intersected elements, the requirementˆh V Dˆh R D N on h is either enforced in a weak sense (e.g., the extended finite element method [36,37]), or in a strong sense (e.g., the immersed boundary discontinuous-Galerkin method, IB-DG [38]). In this work, we assume the use of the IB-DG method and that after such efforts, the electrical boundary value problem can be stated as follows: Findˆ, such that…”

Section: Semi-discrete Formmentioning

confidence: 99%

“…While this gives the full operator for a direct solution of (38), the assembly via (41) is expensive. As advocated in [6], we instead employ the generalized minimal residual method (GMRES) so that only the application of the operator is needed.…”

Section: Direct Solution Of Cyclic Steady Statesmentioning

confidence: 99%

Cyclic steady states of nonlinear electro-mechanical devices excited at resonance

Brandstetter

Govindjee

2016

Int. J. Numer. Meth. Engng

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SUMMARYWe present an efficient numerical method to solve for cyclic steady states of nonlinear electro-mechanical devices excited at resonance. Many electro-mechanical systems are designed to operate at resonance, where the ramp-up simulation to steady state is computationally very expensive -especially when low damping is present. The proposed method relies on a Newton-Krylov shooting scheme for the direct calculation of the cyclic steady state, as opposed to a naïve transient time-stepping from zero initial conditions. We use a recently developed high-order Eulerian-Lagrangian finite element method in combination with an energy-preserving dynamic contact algorithm in order to solve the coupled electro-mechanical boundary value problem. The nonlinear coupled equations are evolved by means of an operator split of the mechanical and electrical problem with an explicit as well as implicit approach. The presented benchmark examples include the first three fundamental modes of a vibrating nanotube, as well as a micro-electro-mechanical disk resonator in dynamic steady contact. For the examples discussed, we observe power law computational speed-ups of the form S D 0:6 0:8 , where is the linear damping ratio of the corresponding resonance frequency.

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“…Neste caso, a dificuldade é transferida para a construção do espaço de multiplicadores. Lew and Buscaglia (2008) apresentaram um método de imposição direta baseado em uma formulação de Galerkin descontínuo, que evita o tratamento caso-a-caso simplesmente trocando a interpolação nas células interceptadas pelo contorno por uma interpolação descontínua, evitando assim o fenômeno de bloqueio (locking). Embora consiga impor fortemente as condições de contorno e obter precisão ótima, o método necessita de graus de liberdade adicionais.…”

Section: Introductionunclassified

Métodos de fronteira imersa em mecânica dos fluidos

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A discontinuous‐Galerkin‐based immersed boundary method

Cited by 93 publications

References 82 publications

A parameter-free variational coupling approach for trimmed isogeometric thin shells

A parameter-free variational coupling approach for trimmed isogeometric thin shells

Cyclic steady states of nonlinear electro-mechanical devices excited at resonance

Métodos de fronteira imersa em mecânica dos fluidos

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