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Higueras Sanz, Inmaculada

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Higueras Sanz

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Inmaculada

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Ingeniería Matemática e Informática

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0000-0003-3860-3360

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288

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2018 - 20193
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Subject: Monotonicity ×

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Now showing 1 - 3 of 3
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    PublicationOpen Access
    Efficient SSP low-storage Runge-Kutta methods
    (2019) Roldán Marrodán, Teodoro; Higueras Sanz, Inmaculada; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
    In this paper we study the efficiency of Strong Stability Preserving (SSP) Runge-Kutta methods that can be implemented with a low number of registers using their Shu-Osher representation. SSP methods have been studied in the literature and stepsize restrictions that ensure numerical monotonicity have been found. However, for some problems, the observed stepsize restrictions are larger than the theoretical ones. Aiming at obtaining additional properties of the schemes that may explain their efficiency, in this paper we study the influence of the local error term in the observed stepsize restrictions. For this purpose, we consider the family of 5-stage third order SSP explicit Runge-Kutta methods, namely SSP(5,3), and the Buckley-Leverett equation. We deal with optimal SSP(5,3) schemes whose implementation requires at least 3 memory registers, and non-optimal 2-register SSP(5,3) schemes. The numerical experiments done show that small error constants improve the efficiency of the method in the sense that larger observed SSP coefficients are obtained.
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    PublicationOpen Access
    Strong stability preserving properties of composition Runge-Kutta schemes
    (Springer, 2019) Higueras Sanz, Inmaculada; Roldán Marrodán, Teodoro; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
    In this paper Strong Stability Preserving (SSP) properties of Runge Kutta methods obtained by com- posing k different schemes with different step sizes are studied. The SSP coefficient of the composition method is obtained and an upper bound on this coefficient is given. Some examples are shown. In par- ticular, it is proven that the optimal n2-stage third order explicit Runge-Kutta methods obtained by D.I. Ketcheson [SIAM J. Sci. Comput. 30(4), 2008] are composition of first order SSP schemes.
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    PublicationOpen Access
    Optimal monotonicity-preserving perturbations of a given Runge–Kutta method
    (Springer, 2018) Higueras Sanz, Inmaculada; Ketcheson, David I.; Kocsis, Tihamér A.; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
    Perturbed Runge–Kutta methods (also referred to as downwind Runge–Kutta methods) can guarantee monotonicity preservation under larger step sizes relative to their traditional Runge–Kutta counterparts. In this paper we study the question of how to optimally perturb a given method in order to increase the radius of absolute monotonicity (a.m.). We prove that for methods with zero radius of a.m., it is always possible to give a perturbation with positive radius. We first study methods for linear problems and then methods for nonlinear problems. In each case, we prove upper bounds on the radius of a.m., and provide algorithms to compute optimal perturbations. We also provide optimal perturbations for many known methods.