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Bart G. van Bloemen Waanders
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Recent Projects
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Current projects:
- Nihilo - A collection of Numerical Interfaces and HIgh Level
Object components for rapid simulation and analysis : The goal of this
project is to develop modular, high level abstraction tools for the
specific purpose of efficiently producing 3D, parallel simulators.
The key idea is to transform high level mathematical notation into
fully functional simulators and avoid the time-consuming
implementation of the underlying services associated with solving
discretized sets of partial differential equations (PDEs). This is
not entirely a new concept as several external and internal activities
have attempted to achieve similar goals. The most notable external
projects (OpenFoam, freefem++, ComSol, PETSc, and Fenics) are based on
high level abstraction ideas with a focus on providing rapid
prototyping simulation capabilities. However, the mission of this
project consists of developing capabilities that can create fully
functional simulators in near-real time with complete access to
analysis algorithms. Furthermore, all the supporting technologies
will be designed in a modular fashion so that components of any
simulator product can be easily interchanged or extended with
specialty code or any component can be used in other simulation
development projects. This is an important point because to achieve
the simulation of complex dynamics coupled to intrusive analysis
algorithms depends on our ability to access virtually every part of
the underlying technology so that non-standard modifications or
extensions can be efficiently implemented. To achieve these goals,
the project will leverage existing high level abstraction C++ concepts
to parse mathematical operators that define dynamics. In the case of
finite element discretization, the operators resulting from the weak
form is the appropriate notational level and our tools will provide
capabilities to write such notation. Minimal code will provide the
infrastructure to connect supporting functionalities, such as boundary
conditions, use of solvers, visualization, etc. Modular design of
sufficiently small components will be accessible through concise
interfaces.
- Reduced Order Modeling: Reduced-order models that are able to
approximate output quantities of interest of high-fidelity
computational models over a wide range of input parameters play an
important role in making tractable large-scale optimal design, optimal
control, and inverse problem applications. This projects considers the problem of
determining a reduced model of an initial value problem that spans all
important initial conditions, and poses the task of determining
appropriate training sets for reduced-basis construction as a sequence
of optimization problems. Under certain assumptions,
these optimization problems have an explicit solution in the form of
an eigenvalue problem, yielding an efficient model reduction algorithm
that scales well to systems with states of high dimension.
- Statistical Inverse problems and Uncertainty Quantification:
In collaboration with Youssef Marzouk I am working on a Bayesian inference
methodology to solve the source inversion problem. We are making use
of the Nihilo/Sundance toolkit which allows for the pseudo-discretization
of the stochastic variables.
- Characterization of biofilms for decontamination:
This project investigates the dynamics of biofilms, which occur in most
aqueous systems including many parts of the human physiology. In collaboration
with Judy Hill, we are using level set methods driven by advection coupled with
diffusion-reaction systems to emulate the nutrient consumption. We formulate
an inverse problem in an attempt to calculate the initial conditions that match
observations of a laboratory grown biofilm.
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