A goal-orientedhp-adaptive finite element method with electromagnetic applications. Part I: electrostatics

Pardo, David; Demkowicz, Leszek; Torres‐Verdín, Carlos; Tabarovsky, L.

doi:10.1002/nme.1488

Cited by 44 publications

(29 citation statements)

References 17 publications

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“…Thus, the corresponding refinement strategy is based on minimizing the error in the quantity of interest rather than an arbitrary energy norm (for details, see Pardo et al, 2006).…”

Section: Hp-fem Approximation Using An Hp-femmentioning

confidence: 99%

An agent-oriented hierarchic strategy for solving inverse problems

Smółka

Schaefer

Paszyński

et al. 2015

International Journal of Applied Mathematics and Computer Science

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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.

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“…Thus, the corresponding refinement strategy is based on minimizing the error in the quantity of interest rather than an arbitrary energy norm (for details, see Pardo et al, 2006).…”

Section: Hp-fem Approximation Using An Hp-femmentioning

confidence: 99%

An agent-oriented hierarchic strategy for solving inverse problems

Smółka

Schaefer

Paszyński

et al. 2015

International Journal of Applied Mathematics and Computer Science

View full text Add to dashboard Cite

show abstract

“…Here, L i (u) is a linear and continuous functional [31,32] in u, which is associated with an scalar component of the EM fields solution at the i-th receiver (occupying a domain Ω R i ).…”

Section: And We Define Hmentioning

confidence: 99%