[EN] A new way to compute the Taylor polynomial of a matrix exponential is presented which reduces the number of matrix multiplications in comparison with the de-facto standard Paterson-Stockmeyer method for polynomial ...
Bader, Philipp Karl Heinz; Blanes Zamora, Sergio; Casas, Fernando; Ponsoda Miralles, Enrique(Elsevier, 2016-01-01)
We consider the numerical integration of high-order linear non-homogeneous differential
equations, written as first order homogeneous linear equations, and using exponential
methods. Integrators like Magnus expansions ...
Bader, Philipp; Blanes Zamora, Sergio; Casas, Fernando; Thalhammer, Mechthild(American Institute of Mathematical Sciences, 2019-12)
[EN] The objective of this work is the introduction and investigation of favourable time integration methods for the Gross-Pitaevskii equation with rotation term. Employing a reformulation in rotating Lagrangian coordinates, ...
Bader, Philipp; Kopylov, Nikita; Blanes Zamora, Sergio(American Institute of Physics, 2018)
[EN] We consider the numerical integration of the Schrodinger equation with a time-dependent Hamiltonian given as the sum of the kinetic energy and a time-dependent potential. Commutator-free (CF) propagators are exponential ...
[EN] We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with ...
Bader, Philipp Karl Heinz(Universitat Politècnica de València, 2011-07-26)
In this work, we address the problem of solving non-linear Schrödinger equations numerically
and find that an exact particular splitting technique shows superior performance to commonly used
methods. We consider the ...
Bader, Philipp Karl-Heinz(Universitat Politècnica de València, 2014-07-11)
The celebrated Schrödinger equation is the key to understanding the dynamics of
quantum mechanical particles and comes in a variety of forms. Its numerical solution
poses numerous challenges, some of which are addressed ...
Kopylov, Nikita(Universitat Politècnica de València, 2019-03-27)
[ES] Esta tesis trata sobre la integración numérica de sistemas hamiltonianos con potenciales explícitamente dependientes del tiempo. Los problemas de este tipo son comunes en la física matemática, porque provienen de la ...
The analysis of heat conduction through a solid with heat generation leads to a linear matrix differential equation with separated boundary conditions. We present a symmetric second order exponential integrator for the ...
[EN] We consider the numerical time-integration of the non-stationary Klein-Gordon equation with position- and time-dependent mass. A novel class of time-averaged symplectic splitting methods involving double commutators ...
[EN] Efficient splitting algorithms for the Schrödinger eigenvalue problem
with perturbed harmonic oscillator potentials in higher dimensions are considered.
The separability of the Hamiltonian makes the problem suitable ...
Bader, Philipp; Blanes Zamora, Sergio; Casas, Fernando(American Institute of Physics (AIP), 2013-09-28)
The Schrodinger eigenvalue problem is solved with the imaginary time propagation technique. The separability of the Hamiltonian makes the problem suitable for the application of splitting methods. High order fractional ...
Seydaoglu, Muaz(Universitat Politècnica de València, 2016-10-07)
[EN] This thesis addresses the treatment of perturbed problems with splitting methods. After motivating these problems in Chapter 1, we give a thorough introduction in Chapter 2, which includes the objectives, several basic ...
Bader, Philipp Karl Heinz; Fischer, U.R.(American Physical Society, 2013-02-28)
We consider spherically trapped Bose gases in three dimensions with contact interactions and investigate whether the Bose-Einstein condensate at zero temperature is stable against macroscopic fragmentation into a small ...
[EN] We present structure preserving integrators for solving linear quadratic optimal control
problems. The goal is to build methods which can also be used for the integration of
nonlinear problems if they are previously ...
[EN] Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise ...
[EN] We consider the numerical integration of the matrix Hill equation. Parametric resonances
can appear and this property is of great interest in many different physical applications.
Usually, Hill s equations originate ...
[EN] New numerical integrators specifically designed for solving the two-body gravitational problem with a time-varying mass are presented. They can be seen as a generalization of commutator-free quasi-Magnus exponential ...
Bader, Philipp; Blanes Zamora, Sergio; Seydaoglu, Muaz(Society for Industrial and Applied Mathematics, 2015)
[EN] We propose splitting methods for the computation of the exponential of perturbed matrices which can be written as the sum A = D+epsilon B of a sparse and efficiently exponentiable matrix D with sparse exponential e(D) ...