INTEGRADORES TEMPORALES. PROPIEDADES CUALITATIVAS Y TECNICAS DE IMPLEMENTACION

MTM2011-23203

Nombre agencia financiadora Ministerio de Ciencia e Innovación
Acrónimo agencia financiadora MICINN
Programa Programa Nacional de Investigación Fundamental
Subprograma Investigación fundamental no-orientada
Convocatoria Investigación Fundamental No-Orientada
Año convocatoria 2011
Unidad de gestión Sin informar
Centro beneficiario UNIVERSIDAD PÚBLICA DE NAVARRA (UPNA)
Centro realización DPTO. DE INGENIERIA MATEMATICA E INFORMATICA
Identificador persistente http://dx.doi.org/10.13039/501100004837

Publicaciones

Found(s) 2 result(s)
Found(s) 1 page(s)

Optimized strong stability preserving IMEX Runge-Kutta methods

Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
  • 0000-0003-3860-3360
  • Happenhofer, Natalie
  • Koch, Othmar
  • Kupka, Friedrich
Esta es la versión no revisada del artículo: Inmaculada Higueras, Natalie Happenhofer, Othmar Koch, and Friedrich Kupka. 2014. Optimized strong stability preserving IMEX Runge-Kutta methods. J. Comput. Appl. Math. 272 (December 2014), 116-140. Se puede consultar la versión final en https://doi.org/10.1016/j.cam.2014.05.011, We construct and analyze robust strong stability preserving IMplicit-EXplicit Runge-Kutta (IMEX RK) methods for models of flow with diffusion as they appear in astrophysics and in many other fields where equations with similar structure arise. It turns out that besides the optimization of the region of absolute monotonicity, some other properties of the methods are crucial for the success of such simulations. In particular, the models in our focus dictate to also take into account the step size limits associated with dissipativity, positivity and the stiff parabolic terms which represent transport by diffusion, the uniform convergence with respect to different stiffness properties of those same terms, etc. Furthermore, in the literature, some other properties, like the inclusion of a part of the imaginary axis in the stability region, have been argued to be relevant. In this paper, we construct several new IMEX RK methods which differ from each other by taking various or even all of these constraints simultaneously into account. It is demonstrated for some simple examples as well as for the problem of double-diffusive convection, that the newly constructed schemes provide a significant computational advantage over other methods from the literature. Due to their accumulation of different stability properties, the optimized IMEX RK methods obtained in this paper are robust schemes that may also be useful for general models which involve the solution of advection-diffusion equations, or other transport equations with similar stability requirements., Inmaculada Higueras was supported by the Ministerio de Ciencia e Innovación, project MTM2011-23203




Construction of additive semi-implicit Runge-Kutta methods with low-storage requirements

Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
  • 0000-0003-3860-3360
  • 0000-0001-8773-3554
The final publication is available at Springer via
http://dx.doi.org/ 10.1007/s10915-015-0116-2, Space discretization of some time-dependent partial differential equations gives rise to systems of
ordinary differential equations in additive form whose terms have different stiffness properties. In these
cases, implicit methods should be used to integrate the stiff terms while efficient explicit methods can be
used for the non-stiff part of the problem. However, for systems with a large number of equations, memory
storage requirement is also an important issue. When the high dimension of the problem compromises
the computer memory capacity, it is important to incorporate low memory usage to some other properties of the scheme.
In this paper we consider Additive Semi-Implicit Runge-Kutta (ASIRK) methods, a class of implicitexplicit
Runge-Kutta methods for additive differential systems. We construct two second order 3-stage
ASIRK schemes with low-storage requirements. Having in mind problems with stiffness parameters,
besides accuracy and stability properties, we also impose stiff accuracy conditions. The numerical experiments done show the advantages of the new methods., Supported by Ministerio de Economía y Competividad, project MTM2011-23203.