
A lowrank LieTrotter splitting approach for nonlinear fractional complex GinzburgLandau equations
Fractional GinzburgLandau equations as the generalization of the classi...
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Numerical methods for differential linear matrix equations via Krylov subspace methods
In the present paper, we present some numerical methods for computing ap...
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A Lowrank Approach for Nonlinear Parameterdependent Fluidstructure Interaction Problems
Parameterdependent discretizations of linear fluidstructure interactio...
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Isogeometric analysis of diffusion problems on random surfaces
In this article, we discuss the numerical solution of diffusion equation...
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A Lowrank Method for Parameterdependent Fluidstructure Interaction Discretizations With Hyperelasticity
In aerospace engineering and boat building, fluidstructure interaction ...
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LargeScale Algebraic Riccati Equations with HighRank Nonlinear Terms and Constant Terms
For largescale discretetime algebraic Riccati equations (DAREs) with h...
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Numerical Analysis for Nematic Electrolytes
We consider a system of nonlinear PDEs modeling nematic electrolytes, an...
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Solving differential Riccati equations: A nonlinear spacetime method using tensor trains
Differential algebraic Riccati equations are at the heart of many applications in control theory. They are timedepent, matrixvalued, and in particular nonlinear equations that require special methods for their solution. Lowrank methods have been used heavily computing a lowrank solution at every step of a timediscretization. We propose the use of an allatonce spacetime solution leading to a large nonlinear spacetime problem for which we propose the use of a NewtonKleinman iteration. Approximating the spacetime problem in lowrank form requires fewer applications of the discretized differential operator and gives a lowrank approximation to the overall solution.
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