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Contact Information
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Institute for Mathematics and its
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Applications (IMA)
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114 Lind Hall, 207 Church Street S.E.
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Minneapolis, MN 55455-0134
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Phone: (612) 626-1815
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| E-mail: trenev@ima.umn.edu
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| WWW:
http://www.ima.umn.edu/~trenev
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| Education
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Texas A&M University, College Station, Texas, USA
- Ph.D., Mathematics, December 2009
- Thesis: Spacial scaling for for the numerical approximation of problems on unbounded domains.
- Advisor: James H. Bramble
Sofia University "St. Kliment Ohridski", Sofia, Bulgaria
- B.S., Mathematics, June 2002
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| Research Interests
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Numerical Methods for Partial Differential Equations, Finite Element Method,
Scientific Computing.
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| Publications and Preprints
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J. Bramble, J. Pasciak and D. Trenev,
Analysis of a Finite PML Approximation to
the Three Dimensional Elastic Wave Scattering Problem,
Math. Comp., 79 (2010).
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| Experience
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Industrial Postdoctoral Associate, Institute for Mathematics and Its Applications, Minneapolis, Minnesota, USA.
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September, 2009 - present |
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Completed a one year industrial internship at ExxonMobil Research and
Engineering Company and derived, implemented and numerically verified
different models of perfectly matched layer (PML) absorbing boundaries
for acoustic wave propagation.
Identified a PML model suitable for discontinuous Galerkin
discretization of the forward wave-propagation problem.
Implemented the model in the setting of seismic waveform inversion.
Investigated the effect of the absorbing boundary conditions on the
inversion.
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Currently completing the second year of my fellowship at the Institute
for Mathematics and Its Applications, where I participate in the
2010-2011 annual program titled ``Simulating Our Complex World:
Modeling, Computation and Analysis'', organize the IMA Postdoc Seminar
and work on comparing the performance of domain-decomposition and
multigrid preconditioning techniques for certain types of
H(div)-based computational problems, as well as on the
development and implementation of an efficient preconditioner for
problems coupling Darcy and Stokes flows.
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Graduate Assistant, Texas A&M University,
College Station, Texas, USA
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August, 2002 - August, 2009 |
| Research Assistant |
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Investigated and developed a numerical algorithm for solving
the elastic wave scattering problem using a PML (complex coordinate shift) approach
for domain truncation. Co-authored a mathematical paper on the subject.
Developed the software implementation of the algorithm, based on the deal.II finite
element library. Conducted various numerical experiments for the PML truncation of
the elastic and acoustic (Helmholtz) scattering problems.
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Analyzed a negative-norm least squares method for the numerical solution of
the eddy-currents problem.
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Analyzed and implemented a real coordinate stretching for effective truncation
of certain elliptic problems posed on infinite domains. Worked on coupling the results
with a negative-norm least-squares method for the eddy-current problem.
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Relevant graduate classes taken : Mathematical Theory of Finite Element Methods,
Theoretical Tools for the Numerical Analysis of PDEs, Multigrid Methods, Mixed Methods,
Computational Software for Large-Scale PDE Solvers, Parallel and Distributed Numerical Algorithms.
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| Instructor of record |
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- Math 131: Mathematical Concepts - Calculus
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Summer 2006 |
| Teaching Assistant |
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- Math 610: Numerical Methods for PDEs
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Spring 2007 and Spring 2008 |
- Math 609: Numerical Analysis
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Fall 2006 and
Fall 2007 |
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Summer 2007 |
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Fall 2005 |
Visiting Instructor,
Sofia University "St. Kliment Ohridski", Sofia, Bulgaria
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January, 2002 - June, 2002 |
- Instructor, Java Network Programming
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Spring 2002 |
Software Engineer (full-time paid internship), Sciant Ltd.
Sofia, Bulgaria
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May, 2000 -
July, 2002 |
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Implementation of certain numerical algorithms for data processing and visualization
components of PI Toolbox - a product of PI Research (UK), targeted for the motor sports
industry.
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Outsource development for Tumbleweed Communications (US). Worked on the customization
of certain aspects of the IMETM software package for Swiss Post.
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Talks and
Presentations
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"Approximating solutions of infinite domain Laplace and Helmholtz problems",
Texas Applied Mathematics Meeting for Students 2009, UT Austin, March 2009.
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"Spatial Scaling for the Exterior Laplace Problem",
Texas Finite Element Rodeo 2009, UT Austin, February 2009.
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"Space Scaling for the Numerical Approximation of Problems on Unbounded Domains",
GSO Seminar, Texas A\&M University, November 2008.
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Conferences
and Workshops
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Numerical Solution of PDEs: Novel Discretization Techniques,
Minneapolis, MN, November 1-5, 2010.
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Texas Finite Element Rodeo 2009, Austin, TX, February 27-28, 2009.
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Workshop on Parallel Numerical Methods for PDEs (RMMC08),
Laramie, WY, June 9-20, 2008.
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Texas Finite Element Rodeo 2006, College Station, TX, March 3-4, 2006.
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8th US National Congress on Computational Mechanics, Austin, TX, July 24-28, 2005.
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Texas Finite Element Rodeo 2004, Austin, TX, March 5-6, 2004.
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Fellowships,
Scholarships
and Awards
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Outstanding Teaching Assistant Award, Texas A&M University, 2007.
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NSF VIGRE Fellowship in the Department of Mathematics, Texas A&M University, 2004-2005.
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AUF Fellowship in the Department of Mathematics, Texas A&M University, 2003-2004.
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Scholarship for Academic Achievement, Sofia University, 1998-2002.
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| Technical Skills
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Languages: Bulgarian (native), English (fluent), Russian (advanced)
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Programming Languages and Libraries: C, C++ (and STL), Java, MPI, deal.II (FEM library)
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Markup Languages: HTML (and CSS), TeX, LaTeX
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Mathematics Software: MatLab, Maple, Mathematica
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