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Laser surface hardening using proper orthogonal decomposition for a threedimensional example
Author(s) -
Hömberg Dietmar,
Volkwein Stefan
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310301
Subject(s) - proper orthogonal decomposition , ordinary differential equation , hardening (computing) , laser , mathematics , work (physics) , heat equation , mathematical analysis , surface (topology) , differential equation , materials science , mechanics , physics , geometry , thermodynamics , optics , composite material , layer (electronics) , turbulence
Laser surface hardening of steel is formulated in terms of an optimal control problem with bilateral control constraints. The state equations are composed of a semilinear heat equation and an ordinary differential equation, which describes the evolution of the high temperature phase. In this work a three‐dimensional example is solved numerically by utilizing model reduction based on proper orthogonal decomposition (POD).