Practical methods for <i>a posteriori</i> error estimation in engineering applications

Multilevel Monte Carlo methods for computing failure probability of porous media flow systems. Advances in Water Resources AbstractWe study improvements of the standard and multilevel Monte Carlo method for point evaluation of the cumulative distribution function (failure probability) applied to porous media two-phase flow simulations with uncertain permeability. To illustrate the methods, we study an injection scenario where we consider sweep efficiency of the injected phase as quantity of interest and seek the probability that this quantity of interest is smaller than a critical value. In the sampling procedure, we use computable error bounds on the sweep efficiency functional to identify small subsets of realizations to solve highest accuracy by means of what we call selective refinement. We quantify the performance gains possible by using selective refinement in combination with both the standard and multilevel Monte Carlo method. We also identify issues in the process of practical implementation of the methods. We conclude that significant savings in computational cost are possible for failure probability estimation in a realistic setting using the selective refinement technique, both in combination with standard and multilevel Monte Carlo.

show abstract

“…See e.g. [2,32] for text books on a posteriori error analysis and [24,26] for two works focusing on estimating errors of goal functionals.…”

Section: Error Bound For Sweep Efficiencymentioning

confidence: 99%

Multilevel Monte Carlo methods for computing failure probability of porous media flow systems

Fagerlund

Hellman

Målqvist

et al. 2016

Advances in Water Resources

View full text Add to dashboard Cite

show abstract

“…We note however that different options are also possible ( see for instance [6,15]). With our choice forφ the optimization over v in (6), leads to…”

Section: Output Boundsmentioning

confidence: 99%

The computation of bounds for linear-functional outputs of weak solutions to the two-dimensional elasticity equations

Mariné

Bonet

Huerta

et al. 2006

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

existence of feasible solutions for the outputs of interest is only given in two dimensions. The computed bound gaps are found to converge optimally, that is, at the same rate as the finite element approximation. An attractive feature of the proposed approach is that it allows for a data set to be generated that can be used to certify and document the computed bounds. Using this data set and a simple algorithm, the correctness of the computed bounds can be established without recourse to the original code used to compute them. In the present paper, only computational domains whose boundary is made up of straight sided segments and polynomially varying loads are considered. Two examples are given to illustrate the proposed methodology.

show abstract

“…To¯nd a compromise, di®erent forms of adaptivity should be exploited. Grid adaptation to the solution can easily be automated, using as stopping criteria (in steady problems) either the speci¯cation of the¯nest grid size [67] or, which is more properly (but more tediously), an error estimation [46]. For the most time consuming part -iterative solution of large sparse systems of equations -one can use an adaptive poly-algorithm (an ordered set of iterative methods from the fast, but the least robust to the most robust slow one) with an automatic method switching [51].…”

Section: Could Software Be User-friendly?mentioning

confidence: 99%

Industrial challenges for numerical simulation of crystal growth

Богданов¹,

Ofengeim²,

Zhmakin³

2004

Open Physics

View full text Add to dashboard Cite

Abstract:Numerical simulation of industrial crystal growth is di¯cult due to its multidisciplinary nature and the complex geometry of the real-life growth equipment. An attempt is made to itemize physical phenomena dominant in the di¬erent methods for growth of bulk crystals from the melt and the vapor phase as well as to review corresponding numerical approaches. Academic research and industrial applications are compared. Development of a computational engine and a graphic user interface of the industry-oriented codes is discussed. A simulator for the entire growth process of bulk crystals by sublimation method is described.

show abstract

Practical methods for a posteriori error estimation in engineering applications

Cited by 55 publications

References 20 publications

Multilevel Monte Carlo methods for computing failure probability of porous media flow systems

Multilevel Monte Carlo methods for computing failure probability of porous media flow systems

The computation of bounds for linear-functional outputs of weak solutions to the two-dimensional elasticity equations

Industrial challenges for numerical simulation of crystal growth

Contact Info

Product

Resources

About