Abstract
The determination of a monotone nonincreasing and convex response function arising in reservoir mechanics is investigated from the computational point of view. Regularization by linear inequalities yields the means for overcoming the ill-posedness of the considered convolution type integral equation. In order to find efficient numerical solutions and adapted approach for solving the associated constrained least squares problems is developed. Some simulation studies complete the paper.
Zusammenfassung
In der Arbeit wird aus numerischer Sicht die Bestimmung einer monoton nichtwachsenden konvexen Responsefunktion untersucht, die in der Reservoirmechanik Anwendung findet. Regularisierung durch lineare Ungleichungen erlaubt die Überwindung der Nichtkorrektheit der betrachteten Faltungs-integralgleichung. Im Sinne effizienter numerischer Lösungen wird ein angepaßter Zugang zur Lösung der entsprechenden restringierten Kleinste-Quadrate-Probleme entwickelt. Einige Simulationsstudien runden die Arbeit ab.
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Hofmann, B., Hausding, R. & Wolke, R. Regularization of a Volterra integral equation by linear inequalities. Computing 43, 361–375 (1990). https://doi.org/10.1007/BF02241655
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DOI: https://doi.org/10.1007/BF02241655