A Fast GPU-Accelerated Mixed-Precision Strategy for Fully Nonlinear Water Wave Computations

Glimberg, Stefan Lemvig; Engsig-Karup, Allan Peter; Madsen, Morten Gorm

doi:10.1007/978-3-642-33134-3_68

Cited by 9 publications

(20 citation statements)

References 7 publications

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“…Another reason to look for alternatives to GMRES is that we target platforms based on modern and emerging architectures and parallel computations on large distributed systems in ongoing work [10,26]. For high performance, this scope warrants minimization of communication patterns [43], for example, by using algorithms with minimal number of global inner products that require global communication [44,45] to secure good scalability on most general-purpose commodity architectures.…”

Section: On Properties Of Existing Iterative Strategies For High-ordementioning

confidence: 99%

“…It is notable that the memory reduction (Section 3.8) achieved by utilizing the PDC method comes at the price of reduced convergence rate compared with the time-constant LU left-preconditioned GMRES method for more strict tolerance levels. Further significant speedup can be achieved in parallel [10,26]. However, the PDC method is found to be increasingly less efficient compared with the GMRES method for the most strict tolerance levels.…”

Section: The Submerged Bar Test (2d)mentioning

confidence: 99%

“…Section 2) to be able to benchmark different algorithmic strategies. This discretization strategy is of particular interest, because it maps efficiently to modern many-core architectures such as graphics processing units [10,26]. For completeness, we mention alternative discretization methods that could also be employed for spatial discretization, for example, boundary element methods (BEMs) [27], also spectral methods [28] or finite element methods (FEMs) [29][30][31][32] including the high-order extension spectralnhp-FEM [33].…”

Section: Discretization Strategymentioning

confidence: 99%

“…Also, there can be performance gains on the order of factors 2 and 1.5, respectively, by exploiting single and mixed-precision computations [10,26] in the iterative solver. The preconditioning solve step should be solved efficiently, for example, by using a time-constant Q L p Q U p -factorization of Q A p in two space dimensions and an efficient geometric MG method in three space dimensions.…”

mentioning

confidence: 99%

“…The preconditioning solve step should be solved efficiently, for example, by using a time-constant Q L p Q U p -factorization of Q A p in two space dimensions and an efficient geometric MG method in three space dimensions. Also, there can be performance gains on the order of factors 2 and 1.5, respectively, by exploiting single and mixed-precision computations [10,26] in the iterative solver. The PDC method without preconditioning requires a total memory workspace of size W DC D 3n for computing the nextˆOE k from the previousˆOE k 1 iterate in the sequence.…”

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confidence: 99%

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Analysis of efficient preconditioned defect correction methods for nonlinear water waves

Engsig-Karup

2014

Numerical Methods in Fluids

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SUMMARYRobust computational procedures for the solution of non‐hydrostatic, free surface, irrotational and inviscid free‐surface water waves in three space dimensions can be based on iterative preconditioned defect correction (PDC) methods. Such methods can be made efficient and scalable to enable prediction of free‐surface wave transformation and accurate wave kinematics in both deep and shallow waters in large marine areas or for predicting the outcome of experiments in large numerical wave tanks. We revisit the classical governing equations are fully nonlinear and dispersive potential flow equations. We present new detailed fundamental analysis using finite‐amplitude wave solutions for iterative solvers. We demonstrate that the PDC method in combination with a high‐order discretization method enables efficient and scalable solution of the linear system of equations arising in potential flow models. Our study is particularly relevant for fast and efficient simulation of non‐breaking fully nonlinear water waves over varying bottom topography that may be limited by computational resources or requirements. To gain insight into algorithmic properties and proper choices of discretization parameters for different PDC strategies, we study systematically limits of accuracy, convergence rate, algorithmic and numerical efficiency and scalability of the most efficient known PDC methods. These strategies are of interest, because they enable generalization of geometric multigrid methods to high‐order accurate discretizations and enable significant improvement in numerical efficiency while incuring minimal storage requirements. We demonstrate robustness using such PDC methods for practical ranges of interest for coastal and maritime engineering, that is, from shallow to deep water, and report details of numerical experiments that can be used for benchmarking purposes. Copyright © 2014 John Wiley & Sons, Ltd.

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Section: On Properties Of Existing Iterative Strategies For High-ordementioning

confidence: 99%

Section: The Submerged Bar Test (2d)mentioning

confidence: 99%

Section: Discretization Strategymentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Analysis of efficient preconditioned defect correction methods for nonlinear water waves

Engsig-Karup

2014

Numerical Methods in Fluids

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An efficient p‐multigrid spectral element model for fully nonlinear water waves and fixed bodies

Engsig-Karup

Laskowski

2021

Numerical Methods in Fluids

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In marine offshore engineering, cost‐efficient simulation of unsteady water waves and their nonlinear interaction with bodies are important to address a broad range of engineering applications at increasing fidelity and scale. We consider a fully nonlinear potential flow (FNPF) model discretized using a Galerkin spectral element method to serve as a basis for handling both wave propagation and wave‐body interaction with high computational efficiency within a single modeling approach. We design and propose an efficient 𝒪(n)‐scalable computational procedure based on geometric p‐multigrid for solving the Laplace problem in the numerical scheme. The fluid volume and the geometric features of complex bodies is represented accurately using high‐order polynomial basis functions and unstructured meshes with curvilinear prism elements. The new p‐multigrid spectral element model can take advantage of the high‐order polynomial basis and thereby avoid generating a hierarchy of geometric meshes with changing number of elements as required in geometric h‐multigrid approaches. We provide numerical benchmarks for the algorithmic and numerical efficiency of the iterative geometric p‐multigrid solver. Results of numerical experiments are presented for wave propagation and for wave‐body interaction in an advanced case for focusing design waves interacting with a floating production storage and offloading. Our study shows, that the use of iterative geometric p‐multigrid methods for the Laplace problem can significantly improve run‐time efficiency of FNPF simulators.

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Efficient uncertainty quantification of a fully nonlinear and dispersive water wave model with random inputs

Bigoni¹,

Engsig-Karup²,

Eskilsson³

2016

J Eng Math

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A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a formulation of a fully nonlinear and dispersive potential flow water wave model with random inputs for the probabilistic description of the evolution of waves. The model is analyzed using random sampling techniques and non-intrusive methods based on generalized Polynomial Chaos (PC). These methods allow to accurately and efficiently estimate the probability distribution of the solution and require only the computation of the solution in different points in the parameter space, allowing for the reuse of existing simulation software. The choice of the applied methods is driven by the number of uncertain input parameters and by the fact that finding the solution of the considered model is computationally intensive. We revisit experimental benchmarks often used for validation of deterministic water wave models. Based on numerical experiments and assumed uncertainties in boundary data, our analysis reveals that some of the known discrepancies from deterministic simulation in comparison with experimental measurements could be partially explained by the variability in the model input. We finally present a synthetic experiment studying the variance based sensitivity of the wave load on an offshore structure to a number of input uncertainties. In the numerical examples presented the PC methods have exhibited fast convergence, suggesting that the problem is amenable to being analyzed with such methods.

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A Fast GPU-Accelerated Mixed-Precision Strategy for Fully Nonlinear Water Wave Computations

Cited by 9 publications

References 7 publications

Analysis of efficient preconditioned defect correction methods for nonlinear water waves

Analysis of efficient preconditioned defect correction methods for nonlinear water waves

An efficient p‐multigrid spectral element model for fully nonlinear water waves and fixed bodies

Efficient uncertainty quantification of a fully nonlinear and dispersive water wave model with random inputs

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