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Browsing by Author "Bader, Philipp Karl Heinz"

Now showing items 1-20 of 21

An efficient algorithm to compute the exponential of skew-Hermitian matrices for the time integration of the Schrodinger equation

Bader, Philipp; Blanes Zamora, Sergio; Casas, Fernando; Seydaoglu, Muaz (Elsevier, 2022-04)

[EN] We present a practical algorithm to approximate the exponential of skew-Hermitian matrices up to round-off error based on an efficient computation of Chebyshev polynomials of matrices and the corresponding error ...
Computing the Matrix Exponential with an Optimized Taylor Polynomial Approximation

Bader, Philipp; Blanes Zamora, Sergio; Casas, Fernando (MDPI AG, 2019-12)

[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 ...
Computing the matrix sine and cosine simultaneously with a reduced number of products

Seydaoglu, Muaz; Bader, Philipp; Blanes Zamora, Sergio; Casas, Fernando (Elsevier, 2021-05)

[EN] A new procedure is presented for computing the matrix cosine and sine simultaneously by means of Taylor polynomial approximations. These are factorized so as to reduce the number of matrix products involved. Two ...
Efficient numerical integration for N th-order non-autonomous linear differential equations

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 ...
Efficient time integration methods for Gross-Pitaevskii equations with rotation term

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, ...
Exponential propagators for the Schrödinger equation with a time-dependent potential

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 ...
Fourier methods for the perturbed harmonic oscillator in linear and nonlinear Schrödinger equations

Bader, Philipp; Blanes Zamora, Sergio (American Physical Society, 2011)

[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 ...
Fourier-Hermite methods for perturbed harmonic oscillator problems

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 ...
Geometric Integrators for Schrödinger Equations

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 ...
Magnus-based geometric integrators for dynamical systems with time-dependent potentials

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 ...
New efficient numerical methods to describe the heat transfer in a solid medium

Ponsoda Miralles, Enrique; Blanes Zamora, Sergio; Bader, Philipp (Elsevier, 2011-10)

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 ...
Novel symplectic integrators for the Klein-Gordon equation with space- and time-dependent mass

Bader, Philipp; Blanes Zamora, Sergio; Casas, Fernando; Kopylov, Nikita (Elsevier, 2019-04)

[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 ...
Solving the Pertubed Quantum Harmonic Oscillator in Imaginary Time Using Splitting Methods with Complex Coefficients

Bader, Philipp; Blanes Zamora, Sergio (Springer, 2014)

[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 ...
Solving the Schrödinger eigenvalue problem by the imaginary time propagation technique using splitting methods with complex coefficients

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 ...
Splitting methods for autonomous and non-autonomous perturbed equations

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 ...
Stability of spherically trapped three-dimensional Bose-Einstein condensates against macroscopic fragmentation

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 ...
Structure preserving integrators for solving (non-)linear quadratic optimal control problems with applications to describe the flight of a quadrotor

Bader, Philipp; Blanes Zamora, Sergio; Ponsoda Miralles, Enrique (Elsevier, 2014-05-15)

[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 ...
Symplectic integrators for second-order linear non-autonomous equations

Bader, Philipp; Blanes Zamora, Sergio; Casas, Fernando; Kopylov, Nikita; Ponsoda Miralles, Enrique (Elsevier, 2018)

[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 ...
Symplectic integrators for the matrix Hill equation

Bader, Philipp; Blanes Zamora, Sergio; Ponsoda Miralles, Enrique; Seydaoglu, Muaz (Elsevier, 2017)

[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 ...
Symplectic propagators for the Kepler problem with time-dependent mass

Bader, Philipp; Blanes Zamora, Sergio; Casas, Fernando; Kopylov, Nikita (Springer-Verlag, 2019-06)

[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 ...