A spectral-in-time Newton–Krylov method for nonlinear PDE-constrained optimization
Keyword(s):
Abstract We devise a method for nonlinear time-dependent partial-differential-equation-constrained optimization problems that uses a spectral-in-time representation of the residual, combined with a Newton–Krylov method to drive the residual to zero. We also propose a preconditioner to accelerate this scheme. Numerical results indicate that this method can achieve fast and accurate solution of nonlinear problems for a range of mesh sizes and problem parameters. The numbers of outer Newton and inner Krylov iterations required to reach the attainable accuracy of a spatial discretization are robust with respect to the number of collocation points in time and also do not change substantially when other problem parameters are varied.
2008 ◽
Vol 11
(4-6)
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pp. 207-219
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2012 ◽
Vol 27
(4-5)
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pp. 625-653
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2014 ◽
Vol 32
(3)
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pp. 272-283
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2014 ◽
Vol 09
(03)
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pp. 203-215