Numerical simulations of multicomponent ecological models with adaptive methods

Adaptive Numerical Methods for Large Scale Simulations and Data Assimilation

Numerical simulation is necessary to understand natural phenomena, make assessments and predictions in various research and engineering fields, develop new technologies, etc. New algorithms are needed to take advantage of the increasing computational resources and utilize the emerging hardware and software infrastructure with maximum efficiency. Adaptive numerical discretization methods can acc...

Numerical Methods 101 - Convergence of Numerical Models

Adaptive numerical components for PDE-based simulations

Numerical simulations based on nonlinear partial differential equations (PDEs) using Newton-based methods require the solution of large, sparse linear systems of equations at each nonlinear iteration. Typically in large-scale parallel simulations such linear systems are solved by using preconditioned Krylov methods. In many cases, especially in time-dependent problems, the attributes of the lin...

Numerical Simulations with Data Assimilation Using an Adaptive POD Procedure

In this study the proper orthogonal decomposition (POD) methodology to model reduction is applied to construct a reduced-order control space for simple advection-diffusion equations. Several 4D-Var data assimilation experiments associated with these models are carried out in the reduced control space. Emphasis is laid on the performance evaluation of an adaptive POD procedure, with respect to t...

Numerical simulations of stellar winds: polytropic models

We discuss steady-state transonic outflows obtained by direct numerical solution of the hydrodynamic and magnetohydrodynamic equations. We make use of the Versatile Advection Code, a software package for solving systems of (hyperbolic) partial differential equations. We proceed stepwise from a spherically symmetric, isothermal, unmagnetized, non-rotating Parker wind to arrive at axisymmetric, p...