I'm Chiara Segala, graduated at University of Verona, Italy. I attended my bachelor's degree in applied mathematics and I am doing now the second year of the master's degree.
I was selected for the GSoC 2016 with the project Exponential Integrators (GNU Octave organization).
Exponential integrators are a class of numerical methods for the solution of partial and ordinary
This is an estimated TIMELINE of my work:
05/05 - 23/05
Study the theory about the exponential Runge-Kutta and Rosenbrock-type integrators:
[HO 10] “Exponential integrators”, Marlis Hochbruck and Alexander Ostermann, 2010, DOI: 10.1017/S0962492910000048
[HO 05] "Explicit exponential Runge-Kutta methods for semilinear parabolic problems", Marlis Hochbruck and Alexander Ostermann, 2005, DOI: 10.1137/040611434, preprint.
Familiarize with the other ODE solvers in Octave, odepkg.
Take a look at
[J 14] “EXPODE - Advanced Exponential Time Integration Toolbox for MATLAB”, Georg Jansing, 2014, webpage.
Study the theory and the features of the expmv code:
[HAM 11] “Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators”, Awad H. Al-Mohy and Nicholas J. Higham, 2011, DOI: 10.1137/100788860.
23/05 - 27/06
week 1 : implementation of phi functions
week 2 : implementation of a scheme for a general exponential Runge-Kutta integrator, see section 2.3 of [HO 10], using the phi functions
week 3 : implementation of a scheme for a general exponential Rosenbrock integrator , see section 2.4 of [HO 10], using the phi functions
week 4 : implementation of a method for the construction of matrix Ã, see theorem 2.1 of [HAM 11]
27/06 - 15/08
week 1-2 : implementation of an advanced method with adaptive time stepping from Runge-Kutta family, using expmv
week 3-4 : implementation of an advanced method with adaptive time stepping from Rosenbrock-type family, using expmv
week 5-6 : implementation of validation tests, e.g. analyze the order of convergence of the methods and some examples
week 7 : add some improvement and code clean up
week 8 : write documentation
15/08 - 22/08 : review of all the work