Non-intrusive Uncertainty Quantification with Sparse Grids for Multivariate Peridynamic Simulations

Franzelin, Fabian; Diehl, Patrick; Pflüger, Dirk

doi:10.1007/978-3-319-06898-5_7

Cited by 10 publications

(7 citation statements)

References 22 publications

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“…A full grid discretization with equidistant mesh width in each dimension of the parameter space, however, is still unfeasible, due to the curse of dimensionality, the effort grows exponentially with the number of dimensions. Sparse grids provide a promising alternative to a full grid discretization and have already been successfully applied to peridynamics (Franzelin et al 2015) in the form of a sensitivity analysis on model parameters. Sparse grids are a numerical method for the approximation of higher-dimensional dependencies that significantly reduces the number of costly simulation runs, without loosing much in the approximation accuracy compared to full grid approaches.…”

Section: Introductionmentioning

confidence: 99%

Bond-based peridynamics: a quantitative study of Mode I crack opening

Diehl¹,

Franzelin²,

Pflüger³

et al. 2016

Int J Fract

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This paper shows a new approach to estimate the critical traction for Mode I crack opening before crack growth by numerical simulation. For quasi-static loading, Linear Elastic Fracture Mechanics predicts the critical traction before crack growth. To simulate the crack growth, we used bond-based peridynamics, a non-local generalization of continuum mechanics. We discretize the peridynamics equation of motion with a collocation by space approach, the socalled EMU nodal discretization. As the constitutive law, we employ the improved prototype micro brittle material model. This bond-based material model is verified by the Young's modulus from classical theory for a homogeneous deformation for different quadrature rules. For the EMU-ND we studied the behavior for different ratios of the horizon and nodal spacing to gain a robust value for a large variety of materials. To access this wide range of materials, we applied sparse grids, a technique to build high-dimensional surrogate models. Sparse grids significantly reduce the number of simulation runs compared to a full grid approach and keep up a similar approximation accuracy. For the validation of the quasi-static loading process, we show that the critical traction is independent of the material density for most material parameters. The bond-based IPMB model with EMU nodal discretization seems very robust for the ratio δ/ΔX = 3 for a wide range of materials, if an error of 5 % is acceptable.

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Section: Introductionmentioning

confidence: 99%

Bond-based peridynamics: a quantitative study of Mode I crack opening

Diehl¹,

Franzelin²,

Pflüger³

et al. 2016

Int J Fract

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“…These are natural questions to ask, and analogous questions have been investigated and answered for several nonlocal and PD models in the absence of fracture, for this case there is now a vast literature; see [65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83]. This work provides the foundation for the numerical analysis of the PD fracture problem.…”

Section: Numerical Analysis For Pd Fracture Modelsmentioning

confidence: 90%

“…This is seen for the EMU nodal discretization [64] which converges to the limit u 0,0 along the diagonal if the nodal spacing decays faster than the horizon [81]. The sensitivity of horizon and nodal spacing are studied in [82,83].…”

Section: Numerical Analysis For Pd Fracture Modelsmentioning

confidence: 99%

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

Diehl¹,

Lipton²,

Wick³

et al. 2021

Preprint

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Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, The Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities with their relative advantages and challenges are summarized.

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“…In the context of UQ, additional options arise to address the outer loop optimisation, because many black-box computer model runs are required. There exist already various techniques such as surrogate models [12][13][14], multifidelity models [15], model order reduction [16], sparse grid interpolation or cubature [17][18][19]. But all these techniques at the end require numerous black-box computer model runs where idling can occur.…”

Section: Introductionmentioning

confidence: 99%

Prediction and reduction of runtime in non-intrusive forward UQ simulations

2019

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To foster predictive simulations, a variety of methods have recently been developed to efficiently tackle uncertainty quantification (UQ) in complex, computational intensive problems. Many of these methods are non-intrusive and, thus, result in a (large) number of embarrassingly parallel black-box evaluations of the underlying simulation codes. While the focus of development is typically on the number of black-box evaluations, which represents the bulk of the computational workload, an additional level of potential performance gains exists. In many scenarios, uncertain input leads not only to uncertain outputs, but also to a varying and thus stochastic runtime of the simulation codes. For scheduling the individual black-box runs, this information is typically not taken into account, resulting in non-negligible idling times on parallel systems. In this contribution, we compare a variety of different scheduling strategies for non-intrusive UQ scenarios using the non-intrusive polynomial chaos approach. In particular, we propose to construct a surrogate model for the runtime of the application using the identical UQ methodology as for the original problem. Using this model to predict the runtimes for subsequent black-box runs allows for (heuristical) optimization of the scheduling. The method has been tested for the forward quantification of uncertainty on academic models and on a pedestrian simulation in the context of evacuation scenarios. This approach allows speed-up factors of about two for the total runtime and can be generalised to a large variety of applications that incorporate parameter-dependent runtime.

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Non-intrusive Uncertainty Quantification with Sparse Grids for Multivariate Peridynamic Simulations

Cited by 10 publications

References 22 publications

Bond-based peridynamics: a quantitative study of Mode I crack opening

Bond-based peridynamics: a quantitative study of Mode I crack opening

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

Prediction and reduction of runtime in non-intrusive forward UQ simulations

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