Computing the First Eigenpair of the p-Laplacian via Inverse Iteration of Sublinear Supersolutions

Biezuner, Rodney Josué; Brown, Jed; Ercole, Grey; Martins, Eder Marinho

doi:10.1007/s10915-011-9540-0

Cited by 23 publications

(22 citation statements)

References 38 publications

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“…This capability is the basis for solution transfer being developed as part of the SHARP application discussed in Section 2.1.3 and also has been used to transfer radiation heat deposition results from the MCNP code (Brown, 2012) to a tetrahedral mesh for heat transfer/fluid flow computations (Sawan et al, 2009). Additional MOAB applications include Nek5000 (Fischer et al, 2012), the Denovo neutron transport code (Evans et al, 2010), and an ice sheet modeling code (Biezuner et al, 2012;Brown, 2010).…”

mentioning

confidence: 99%

Multiphysics simulations: challenges and opportunities.

Keyes¹,

McInnes²,

Woodward³

et al. 2012

149

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We consider multiphysics applications from algorithmic and architectural perspectives, where "algorithmic" includes both mathematical analysis and computational complexity and "architectural" includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not always practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities.

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mentioning

confidence: 99%

Multiphysics simulations: challenges and opportunities.

Keyes¹,

McInnes²,

Woodward³

et al. 2012

149

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“…The solid curve for N = 1 depicts the exact value (1.3). For N = 2, 3 and 4 the thick dots represent approximate values of λ 1 for certain discrete values of p, which were evaluated in [6]. The dashed curves represent lower and upper estimates from (1.5), the dotted curves visualize those from (1.6).…”

Section: P-laplacianmentioning

confidence: 99%

Estimates of the principal eigenvalue of the $p$-Laplacian and the $p$-biharmonic operator

Benedikt¹

2015

Math. Bohem.

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We survey recent results concerning estimates of the principal eigenvalue of the Dirichlet p-Laplacian and the Navier p-biharmonic operator on a ball of radius R in R N and its asymptotics for p approaching 1 and ∞. Let p tend to ∞. There is a critical radius R C of the ball such that the principal eigenvalue goes to ∞ for 0 < R R C and to 0 for R > R C. The critical radius is R C = 1 for any N ∈ N for the p-Laplacian and R C = √ 2N in the case of the p-biharmonic operator. When p approaches 1, the principal eigenvalue of the Dirichlet p-Laplacian is N R −1 × (1 − (p − 1) log R(p − 1)) + o(p − 1) while the asymptotics for the principal eigenvalue of the Navier p-biharmonic operator reads 2N/R 2 + O(−(p − 1) log(p − 1)).

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“…This capability is the basis for solution transfer being developed as part of the SHARP application discussed in Section 2.1.3 and also has been used to transfer radiation heat deposition results from the MCNP code (Brown, 2012) to a tetrahedral mesh for heat transfer/fluid flow computations (Sawan et al, 2009). Additional MOAB applications include Nek5000 (Fischer et al, 2012), the Denovo neutron transport code (Evans et al, 2010), and an ice-sheet modeling code (Brown, 2010; Biezuner et al, 2012).…”

Section: Multiphysics Softwarementioning

confidence: 99%

Multiphysics simulations

Keyes

McInnes

Woodward

et al. 2013

The International Journal of High Performance Computing Applica

Self Cite

277

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We consider multiphysics applications from algorithmic and architectural perspectives, where “algorithmic” includes both mathematical analysis and computational complexity, and “architectural” includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not always practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities.

show abstract

Computing the First Eigenpair of the p-Laplacian via Inverse Iteration of Sublinear Supersolutions

Cited by 23 publications

References 38 publications

Multiphysics simulations: challenges and opportunities.

Multiphysics simulations: challenges and opportunities.

Estimates of the principal eigenvalue of the $p$-Laplacian and the $p$-biharmonic operator

Multiphysics simulations

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