Sökning: "exponential integrators"

Visar resultat 1 - 5 av 7 avhandlingar innehållade orden exponential integrators.

  1. 1. Exponential integrators for stochastic partial differential equations

    Författare :Rikard Anton; David Cohen; Christian Engström; Stig Larsson; Annika Lang; Umeå universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Stochastic partial differential equations; numerical methods; stochastic exponential integrator; strong convergence; trace formulas;

    Sammanfattning : Stochastic partial differential equations (SPDEs) have during the past decades become an important tool for modeling systems which are influenced by randomness. Because of the complex nature of SPDEs, knowledge of efficient numerical methods with good convergence and geometric properties is of considerable importance. LÄS MER

  3. 2. Adaptive Solvers for High-Dimensional PDE Problems on Clusters of Multicore Processors

    Författare :Magnus Grandin; Sverker Holmgren; Michael Thuné; Michael Bader; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; adaptive mesh refinement; anisotropic refinement; exponential integrators; Lanczos algorithm; hybrid parallelization; time-dependent Schrödinger equation; Scientific Computing; Beräkningsvetenskap;

    Sammanfattning : Accurate numerical solution of time-dependent, high-dimensional partial differential equations (PDEs) usually requires efficient numerical techniques and massive-scale parallel computing. In this thesis, we implement and evaluate discretization schemes suited for PDEs of higher dimensionality, focusing on high order of accuracy and low computational cost. LÄS MER

  4. 3. Efficient and Reliable Simulation of Quantum Molecular Dynamics

    Författare :Katharina Kormann; Sverker Holmgren; Gunilla Kreiss; Hans O. Karlsson; Christian Lubich; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; time-dependent Schrödinger equation; quantum optimal control; exponential integrators; spectral elements; radial basis functions; global error control and adaptivity; high-performance computing implementation; Beräkningsvetenskap med inriktning mot numerisk analys; Scientific Computing with specialization in Numerical Analysis;

    Sammanfattning : The time-dependent Schrödinger equation (TDSE) models the quantum nature of molecular processes.  Numerical simulations based on the TDSE help in understanding and predicting the outcome of chemical reactions. LÄS MER

  5. 4. Numerical analysis and simulation of stochastic partial differential equations with white noise dispersion

    Författare :André Berg; David Cohen; Per Åhag; Guillaume Dujardin; Ludovic Goudenège; Umeå universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; stochastic partial differential equation; mathematics; numerical analysis; numerical scheme; time integrator; convergence analysis; blowup; critical exponent; nonlinear Schrödinger equation; Manakov equation; Benjamin-Bona-Mahony equation; BBM equation; stochastic; random; dispersion; white noise dispersion; finite difference; pseudospectral; code; matlab; exponential integrator; splitting integrator; convergence in probability; Mathematics; matematik; Numerical Analysis; numerisk analys;

    Sammanfattning : This doctoral thesis provides a comprehensive numerical analysis and exploration of several stochastic partial differential equations (SPDEs). More specifically, this thesis investigates time integrators for SPDEs with white noise dispersion. LÄS MER

  7. 5. Towards an adaptive solver for high-dimensional PDE problems on clusters of multicore processors

    Författare :Magnus Gustafsson; Sverker Holmgren; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Scientific Computing; Beräkningsvetenskap;

    Sammanfattning : Accurate numerical simulation of time-dependent phenomena in many spatial dimensions is a challenging computational task apparent in a vast range of application areas, for instance quantum dynamics, financial mathematics, systems biology and plasma physics. Particularly problematic is that the number of unknowns in the governing equations (the number of grid points) grows exponentially with the number of spatial dimensions introduced, often referred to as the curse of dimensionality. LÄS MER