An approximate block Newton method for coupled iterations of nonlinear solvers: Theory and conjugate heat transfer applications

Yeckel, Andrew; Lun, Lisa; Derby, Jeffrey J.

doi:10.1016/j.jcp.2009.08.003

Cited by 30 publications

(33 citation statements)

References 19 publications

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“…This important specialization facilitates use of an inexact Newton method by eliminating the need to identify and implement the Jacobian. Of course, efficiency of JFNK depends critically on preconditioning the inner Krylov subspace method, and the need to track changes in the Jacobian places a premium on preconditioners with low setup cost; see (Knoll and Keyes, 2004;Anderson et al, 1999;Gropp et al, 2000;Pernice and Tocci, 2001;Chacón and Knoll, 2003;Mousseau, 2004;Knoll et al, 2005;Reynolds et al, 2006;Yeckel et al, 2009). Implementations of inexact Newton methods are available in several high-performance software libraries Heroux et al, 2005;Hindmarsh et al, 2005).…”

Section: Methods For Systems Of Nonlinear Equationsmentioning

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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Section: Methods For Systems Of Nonlinear Equationsmentioning

confidence: 99%

Multiphysics simulations: challenges and opportunities.

Keyes¹,

McInnes²,

Woodward³

et al. 2012

149

View full text Add to dashboard Cite

show abstract

“…However, in that case this approach can become very expensive unless the matrices in the direct solver do not have to be factorized again for each calculation. Yeckel et al [203] analyzed the special case where the iterative solvers are Newton solvers and developed the approximate block Newton (ABN) method and variations on the ATBN method with block diagonal preconditioners.…”

Section: : Solvementioning

confidence: 99%

“…Yeckel et al [203] solve conjugate heat transfer problems that represent melt crystal growth processes. Therefore, they couple a furnace radiation model with a melt crystal growth model using the ABN method.…”

Section: Other Coupled Problemsmentioning

confidence: 99%

Partitioned Simulation of Fluid-Structure Interaction

Degroote¹

2013

Arch Computat Methods Eng

124

107

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In this review article, the focus is on partitioned simulation techniques for strongly coupled fluid-structure interaction problems, especially on techniques which use at least one of the solvers as a black box. First, a number of analyses are reviewed to explain why Gauss-Seidel coupling iterations converge slowly or not at all for fluid-structure interaction problems with strong coupling. This provides the theoretical basis for the fast convergence of quasi-Newton and multi-level techniques. Second, several partitioned techniques that couple two black-box solvers are compared with respect to implementation and performance. Furthermore, performance comparisons between partitioned and monolithic techniques are examined. Subsequently, two similar techniques to couple a black-box solver with an accessible solver are analyzed. In addition, several other techniques for fluid-structure interaction simulations are studied and various methods to take into account deforming fluid domains are discussed.

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“…An alternative approach that maintains the quadratic convergence of Newton's method, but allows for greater flexibility in the choice of solver for each system component is nonlinear elimination. Nonlinear elimination has been used in circuit simulation [16,23] (also called the "Two-level Newton" technique in the circuit community), aerostructures [29], and chemically reacting flows [28]. A theoretical analysis with convergence proofs can be found in [13,27].…”

Section: Nonlinear Eliminationmentioning

confidence: 99%

“…Given a group of multi-physics applications to couple, many variations and combinations of nonlinear elimination and other solution strategies can be employed to achieve a convergent system. The approximate block Newton methods analyzed in [28] are a good example. is defined to be another name for y.…”

Section: Nonlinear Eliminationmentioning

confidence: 99%

A theory manual for multi-physics code coupling in LIME.

Belcourt¹,

Bartlett²,

Pawlowski³

et al. 2011

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The Lightweight Integrating Multi-physics Environment (LIME) is a software package for creating multi-physics simulation codes. Its primary application space is when computer codes are currently available to solve different parts of a multi-physics problem and now need to be coupled with other such codes. In this report we define a common domain language for discussing multi-physics coupling and describe the basic theory associated with multiphysics coupling algorithms that are to be supported in LIME. We provide an assessment of coupling techniques for both steady-state and time dependent coupled systems. Example couplings are also demonstrated.iii

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An approximate block Newton method for coupled iterations of nonlinear solvers: Theory and conjugate heat transfer applications

Cited by 30 publications

References 19 publications

Multiphysics simulations: challenges and opportunities.

Multiphysics simulations: challenges and opportunities.

Partitioned Simulation of Fluid-Structure Interaction

A theory manual for multi-physics code coupling in LIME.

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