12 research outputs found
Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part II: application to partial differential equations
A template-based generic programming approach was presented in a previous
paper that separates the development effort of programming a physical model
from that of computing additional quantities, such as derivatives, needed for
embedded analysis algorithms. In this paper, we describe the implementation
details for using the template-based generic programming approach for
simulation and analysis of partial differential equations (PDEs). We detail
several of the hurdles that we have encountered, and some of the software
infrastructure developed to overcome them. We end with a demonstration where we
present shape optimization and uncertainty quantification results for a 3D PDE
application
Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part I: template-based generic programming
An approach for incorporating embedded simulation and analysis capabilities
in complex simulation codes through template-based generic programming is
presented. This approach relies on templating and operator overloading within
the C++ language to transform a given calculation into one that can compute a
variety of additional quantities that are necessary for many state-of-the-art
simulation and analysis algorithms. An approach for incorporating these ideas
into complex simulation codes through general graph-based assembly is also
presented. These ideas have been implemented within a set of packages in the
Trilinos framework and are demonstrated on a simple problem from chemical
engineering
Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces
In this paper we present computational techniques to investigate the
solutions of two-component, nonlinear reaction-diffusion (RD) systems on
arbitrary surfaces. We build on standard techniques for linear and nonlinear
analysis of RD systems, and extend them to operate on large-scale meshes for
arbitrary surfaces. In particular, we use spectral techniques for a linear
stability analysis to characterize and directly compose patterns emerging from
homogeneities. We develop an implementation using surface finite element
methods and a numerical eigenanalysis of the Laplace-Beltrami operator on
surface meshes. In addition, we describe a technique to explore solutions of
the nonlinear RD equations using numerical continuation. Here, we present a
multiresolution approach that allows us to trace solution branches of the
nonlinear equations efficiently even for large-scale meshes. Finally, we
demonstrate the working of our framework for two RD systems with applications
in biological pattern formation: a Brusselator model that has been used to
model pattern development on growing plant tips, and a chemotactic model for
the formation of skin pigmentation patterns. While these models have been used
previously on simple geometries, our framework allows us to study the impact of
arbitrary geometries on emerging patterns.Comment: This paper was submitted at the Journal of Mathematical Biology,
Springer on 07th July 2015, in its current form (barring image references on
the last page and cosmetic changes owning to rebuild for arXiv). The complete
body of work presented here was included and defended as a part of my PhD
thesis in Nov 2015 at the University of Ber
Numerical bifurcation analysis of pattern formation in a cell based auxin transport model
Transport models of growth hormones can be used to reproduce the hormone
accumulations that occur in plant organs. Mostly, these accumulation patterns
are calculated using time step methods, even though only the resulting steady
state patterns of the model are of interest. We examine the steady state
solutions of the hormone transport model of Smith et al (2006) for a
one-dimensional row of plant cells. We search for the steady state solutions as
a function of three of the model parameters by using numerical continuation
methods and bifurcation analysis. These methods are more adequate for solving
steady state problems than time step methods. We discuss a trivial solution
where the concentrations of hormones are equal in all cells and examine its
stability region. We identify two generic bifurcation scenarios through which
the trivial solution loses its stability. The trivial solution becomes either a
steady state pattern with regular spaced peaks or a pattern where the
concentration is periodic in time.Comment: submitte
Diagramas de bifurcación con interfaz gráfica
Universidad de Sevilla. Máster en IngenierÃa de Caminos, Canales y Puerto
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Solution-verified reliability analysis and design of bistable MEMS using error estimation and adaptivity.
This report documents the results for an FY06 ASC Algorithms Level 2 milestone combining error estimation and adaptivity, uncertainty quantification, and probabilistic design capabilities applied to the analysis and design of bistable MEMS. Through the use of error estimation and adaptive mesh refinement, solution verification can be performed in an automated and parameter-adaptive manner. The resulting uncertainty analysis and probabilistic design studies are shown to be more accurate, efficient, reliable, and convenient