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Subject: numerics × WGL Institute: WIAS ×

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Now showing 1 - 4 of 4
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    Time discretization and Markovian iteration for coupled FBSDEs
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Bender, Christian; Zhang, Jianfeng
    In this paper we lay the foundation for a numerical algorithm to simulate high-dimensional coupled FBSDEs under weak coupling or monotonicity conditions. In particular we prove convergence of a time discretization and a Markovian iteration. The iteration differs from standard Picard iterations for FBSDEs in that the dimension of the underlying Markovian process does not increase with the number of iterations. This feature seems to be indispensable for an efficient iterative scheme from a numerical point of view. We finally suggest a fully explicit numerical algorithm and present some numerical examples with up to 10-dimensional state space.
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    A modeling framework for efficient reduced order simulations of parametrized lithium-ion battery cells
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Landstorfer, Manuel; Ohlberger, Mario; Rave, Stephan; Tacke, Marie
    In this contribution we present a new modeling and simulation framework for parametrized Lithium-ion battery cells. We first derive a new continuum model for a rather general intercalation battery cell on the basis of non-equilibrium thermodynamics. In order to efficiently evaluate the resulting parameterized non-linear system of partial differential equations the reduced basis method is employed. The reduced basis method is a model order reduction technique on the basis of an incremental hierarchical approximate proper orthogonal decomposition approach and empirical operator interpolation. The modeling framework is particularly well suited to investigate and quantify degradation effects of battery cells. Several numerical experiments are given to demonstrate the scope and efficiency of the modeling framework.
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    Identification of the thermal growth characteristics of coagulated tumor tissue in laser-induced thermotherapy
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Hömberg, Dietmar; Liu, Jujun; Togobytska, Nataliya
    We consider an inverse problem arising in laser-induced thermotherapy, a minimally invasive method for cancer treatment, in which cancer tissues is destroyed by coagulation. For the dosage planning numerical simulation play an important role. To this end a crucial problem is to identify the thermal growth kinetics of the coagulated zone. Mathematically, this problem is a nonlinear and nonlocal parabolic heat source inverse problem. The solution to this inverse problem is defined as the minimizer of a nonconvex cost functional. The existence of the minimizer is proven. We derive the Gateaux derivative of the cost functional, which is based on the adjoint system, and use it for a numerical approximation of the optimal coefficient.
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    Numerics of thin-film free boundary problems for partial wetting
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Peschka, Dirk
    We present a novel framework to solve thin-film equations with an explicit non-zero contact angle, where the support of the solution is treated as an unknown. The algorithm uses a finite element method based on a gradient formulation of the thin-film equations coupled to an arbitrary Lagrangian-Eulerian method for the motion of the support. Features of this algorithm are its simplicity and robustness. We apply this algorithm in 1D and 2D to problems with surface tension, contact angles and with gravity.