scholarly journals An agent-oriented hierarchic strategy for solving inverse problems

2015 ◽  
Vol 25 (3) ◽  
pp. 483-498 ◽  
Author(s):  
Maciej Smołka ◽  
Robert Schaefer ◽  
Maciej Paszyński ◽  
David Pardo ◽  
Julen Álvarez-Aramberri
Keyword(s):  
Inverse Problems ◽  
Computational Cost ◽  
Real Life ◽  
Engineering Problem ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Two Phase ◽  
Magnetotelluric Data ◽  
Complex Agent ◽  
Evolutionary Technique

Abstract The paper discusses the complex, agent-oriented hierarchic memetic strategy (HMS) dedicated to solving inverse parametric problems. The strategy goes beyond the idea of two-phase global optimization algorithms. The global search performed by a tree of dependent demes is dynamically alternated with local, steepest descent searches. The strategy offers exceptionally low computational costs, mainly because the direct solver accuracy (performed by the hp-adaptive finite element method) is dynamically adjusted for each inverse search step. The computational cost is further decreased by the strategy employed for solution inter-processing and fitness deterioration. The HMS efficiency is compared with the results of a standard evolutionary technique, as well as with the multi-start strategy on benchmarks that exhibit typical inverse problems’ difficulties. Finally, an HMS application to a real-life engineering problem leading to the identification of oil deposits by inverting magnetotelluric measurements is presented. The HMS applicability to the inversion of magnetotelluric data is also mathematically verified.

Two-dimensional Bayesian inversion of magnetotelluric data using trans-dimensional Gaussian processes

2021 ◽  
Author(s):  
Daniel Blatter ◽  
Anandaroop Ray ◽  
Kerry Key
Keyword(s):  
Gaussian Process ◽  
Process Model ◽  
Field Data ◽  
Probability Distributions ◽  
Bulk Composition ◽  
Computational Cost ◽  
Model Space ◽  
Bayesian Inversion ◽  
Adaptive Finite Element ◽  
Magnetotelluric Data

Summary Bayesian inversion of electromagnetic data produces crucial uncertainty information on inferred subsurface resistivity. Due to their high computational cost, however, Bayesian inverse methods have largely been restricted to computationally expedient 1D resistivity models. In this study, we successfully demonstrate, for the first time, a fully 2D, trans-dimensional Bayesian inversion of magnetotelluric data. We render this problem tractable from a computational standpoint by using a stochastic interpolation algorithm known as a Gaussian process to achieve a parsimonious parametrization of the model vis-a-vis the dense parameter grids used in numerical forward modeling codes. The Gaussian process links a trans-dimensional, parallel tempered Markov chain Monte Carlo sampler, which explores the parsimonious model space, to MARE2DEM, an adaptive finite element forward solver. MARE2DEM computes the model response using a dense parameter mesh with resistivity assigned via the Gaussian process model. We demonstrate the new trans-dimensional Gaussian process sampler by inverting both synthetic and field magnetotelluric data for 2D models of electrical resistivity, with the field data example converging within 10 days on 148 cores, a non-negligible but tractable computational cost. For a field data inversion, our algorithm achieves a parameter reduction of over 32x compared to the fixed parameter grid used for the MARE2DEM regularized inversion. Resistivity probability distributions computed from the ensemble of models produced by the inversion yield credible intervals and interquartile plots that quantitatively show the non-linear 2D uncertainty in model structure. This uncertainty could then be propagated to other physical properties that impact resistivity including bulk composition, porosity and pore-fluid content.

Phase-Field Numerical Simulation of Pure Free Dendritic Growth Using Wheeler and Karma Model

2011 ◽  
Vol 421 ◽  
pp. 90-97 ◽  
Author(s):  
Yun Chen ◽  
Na Min Xiao ◽  
Xiu Hong Kang ◽  
Dian Zhong Li
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Dendrite Growth ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Two Phase ◽  
Phase Field Models ◽  
Careful Comparison ◽  
Undercooled Melts

To understand the dendrite formation during solidification phase-field model has become a powerful numerical method of simulating crystal growth in recent years. Two phase-field models due to Wheeler et al. and Karma et al., respectively, have been employed for modeling the dendrite growth worldwidely. The comparison of the two models was performed. Then using the adaptive finite element method, both models were solved to simulate a free dendrite growing from highly undercooled melts of nickel at various undercoolings. The simulated results showed that the discrepancy between the two phase-field models is negligible. Careful comparison of the phase-filed simulations with LKT(BCT) theory and experimental data were carried out, which demonstrated that the phase-field models are able to quantitatively simulate the dendrite growth of nickel at low undercoolings, however, at undercoolings above ten percent of the melting point (around 180K), the simulated velocities by Wheeler and Karma model as well as the analytical predictions overestimated the reported experiment results.

scholarly journals Applications of A Hyper–Graph Grammar System in Adaptive Finite–Element Computations

2018 ◽  
Vol 28 (3) ◽  
pp. 569-582 ◽  
Author(s):  
Piotr Gurgul ◽  
Konrad Jopek ◽  
Keshav Pingali ◽  
Anna Paszyńska
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computational Cost ◽  
Three Dimensional ◽  
Parallel Execution ◽  
Graph Grammar ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Grammar System ◽  
Element Method

Abstract This paper describes application of a hyper-graph grammar system for modeling a three-dimensional adaptive finite element method. The hyper-graph grammar approach allows obtaining a linear computational cost of adaptive mesh transformations and computations performed over refined meshes. The computations are done by a hyper-graph grammar driven algorithm applicable to three-dimensional problems. For the case of typical refinements performed towards a point or an edge, the algorithm yields linear computational cost with respect to the mesh nodes for its sequential execution and logarithmic cost for its parallel execution. Such hyper-graph grammar productions are the mathematical formalism used to describe the computational algorithm implementing the finite element method. Each production indicates the smallest atomic task that can be executed concurrently. The mesh transformations and computations by using the hyper-graph grammar-based approach have been tested in the GALOIS environment. We conclude the paper with some numerical results performed on a shared-memory Linux cluster node, for the case of three-dimensional computational meshes refined towards a point, an edge and a face.

scholarly journals Element Partition Trees For H-Refined Meshes to Optimize Direct Solver Performance. Part I: Dynamic Programming

2017 ◽  
Vol 27 (2) ◽  
pp. 351-365 ◽  
Author(s):  
Hassan Aboueisha ◽  
Victor Manuel Calo ◽  
Konrad Jopek ◽  
Mikhail Moshkov ◽  
Anna Paszyńka ◽  
...  
Keyword(s):  
Dynamic Programming ◽  
Heuristic Algorithm ◽  
Heuristic Algorithms ◽  
Computational Cost ◽  
Adaptive Finite Element Method ◽  
Programming Approach ◽  
Adaptive Finite Element ◽  
Adaptive Grids ◽  
Dynamic Programming Approach ◽  
Refined Meshes

AbstractWe consider a class of two- and three-dimensional h-refined meshes generated by an adaptive finite element method. We introduce an element partition tree, which controls the execution of the multi-frontal solver algorithm over these refined grids. We propose and study algorithms with polynomial computational cost for the optimization of these element partition trees. The trees provide an ordering for the elimination of unknowns. The algorithms automatically optimize the element partition trees using extensions of dynamic programming. The construction of the trees by the dynamic programming approach is expensive. These generated trees cannot be used in practice, but rather utilized as a learning tool to propose fast heuristic algorithms. In this first part of our paper we focus on the dynamic programming approach, and draw a sketch of the heuristic algorithm. The second part will be devoted to a more detailed analysis of the heuristic algorithm extended for the case of hp-adaptive grids.

A two-phase adaptive finite element method for solid-fluid coupling in complex geometries

2011 ◽  
Vol 66 (1) ◽  
pp. 82-96 ◽  
Author(s):  
Xavier García ◽  
Dimitrios Pavlidis ◽  
Gerard J. Gorman ◽  
Jefferson L. M. A. Gomes ◽  
Matthew D. Piggott ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Adaptive Finite Element Method ◽  
Complex Geometries ◽  
Adaptive Finite Element ◽  
Two Phase ◽  
Fluid Coupling ◽  
Solid Fluid Coupling ◽  
Element Method

A Hybrid Numerical Model for Simulating Atmospheric Dispersion

2005 ◽  
Author(s):  
Xiuling Wang ◽  
Darrell W. Pepper
Keyword(s):  
Numerical Model ◽  
Particle Transport ◽  
Numerical Solutions ◽  
Computational Cost ◽  
Adaptive Finite Element Method ◽  
Computational Error ◽  
Random Component ◽  
Adaptive Finite Element ◽  
Contaminant Dispersion ◽  
Fine Mesh

A hybrid numerical model for simulating atmospheric contaminant dispersion is developed. The hybrid numerical scheme employs an hp-adaptive finite element method coupled with a Lagrangian particle transport technique to solve the governing equations for atmospheric flow and species transport. A random walk/stochastic approach is used to generate Lagrangian particles that define the contaminant dispersion traces. A coarse mesh using low order shape functions is initially generated. Both the mesh and shape function order are subsequently refined and enriched in those regions where high computational error exist. Compared with fine mesh and high order numerical solutions, the hybrid scheme produces highly accurate solutions with reduced computational cost. A general probability distribution is used in the particle transport module for the random component of motion due to turbulent diffusion. Results depicting contaminant transport and dispersion in the atmosphere are presented. The computational efficiency of the hybrid numerical model is also discussed.

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