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Felina Users and Their Projects

UTEP's hp-FEM group - Development of theory and algorithms for scalable higher-order finite element methods (hp-FEM) for partial differential equations. Automatic hp-adaptivity. Parallelization. Application to solid anf fluid mechanics, electromagnetics, and nonlinear multiscale coupled problems.

• Pavel Solin: Computer simulation of large-scale nonlinear coupled problems.

EXAMPLE: 3D model of induction heating of a 3D metallic object (electromagnetic field + nonstationary heat transfer).

EXAMPLE: 3D axisymmetric model of electromagnetic stirring of a molten metal (electromagnetic field + viscous flow).

EXAMPLE: Output of parallel unstructured tetrahedral mesh generator XGEN_3D developed by the hp-FEM group.

• Jakub Cerveny: Investigation of multiple level constrained approximation algorithms in the hp-FEM and their relation to automatic hp-adaptivity.

EXAMPLE: Higher-order finite element basis function on a mesh with multiple constraints.

* Martin Lazar: Investigation of parallel data structures for hp-FEM,

parallel domain decomposition algorithms, parallelization of hp-FEM.

EXAMPLE: Decomposition of hp-FEM mesh of a 3D object.

• Tomas Vejchodsky: hp-FEM for time-harmonic Maxwell's equations

EXAMPLE: Singularity of scattered electric field at a re-entrant corner.

• Martin Zitka: Development of theory and scalable algorithms for hp-FEM in 3D.

EXAMPLE: Magnitude of electric field strength in the Fichera corner domain.

• Jose Avila: Development of advanced techniques for the approximation of boundary layers in fluids based on the hp-FEM.

[EXAMPLE: Thin boundary layer on the wing of a flying airplane.]

Tunna Baruah - Investigation of electronic, structural, magnetic, optical, vibrational, and other properties of materials, single-molecule magnets, inorganic fullerenes, and clusters, based on massive parallel simulations of multi-molecule models.

EXAMPLE: Light-harvesting molecule designed using Density Functional Theory (DFT).

Raul Cruz - Use of machine learning methods, such as artificial neural networks, support vector machines, fuzzy logic and genetic algorithms, to solve different Bioinformatics classification problems.

EXAMPLE: Clusters of replication origins of herpesviruses.

Murat Durandurdu - condensed matter theory and computational materials physics. I use quantum mechanical computer simulations based on density functional theory to explore the fundamental principles of nano, crystal and amorphous structures and their behavior under external conditions such as at high pressures and temperatures.

EXAMPLE: Evolution of the rocksalt structure form the wurtzite structure under pressure (a) wurzite phase (b) hexagonal phase (c) Cmcm phase (d)distorted rocksalt phase.

Christian Escudero - Representations of the Figure Eight Knot (a computational topology project). A knot in the 3-sphere is universal if any connected closed orientable 3-manifold is a branched cover of the 3-sphere with branch set the given knot. All the known examples of knots that are not universal have zero volume. The connected sum K of the figure 8 knot K_0 with itself has nonzero volume, and it is not known if K is universal or not. By work of Victor Nunez and Enrique Ramirez-Losada, for K to not be universal it suffices to show understand certain representations of the fundamental group of K_0 in the symmetric groups S_n. Our project consists in constructing such representations via a computer program like GAP; the patterns we look for require the classification of representations for n>29, which require a substantial amount of computational and memory resources. We expect to reach the level n=36 with the current software and computer resources.

Ming-Ying Leung - Computational analysis of biomolecular sequences: Design of computational algorithms and development of statistical criteria to help identify nonrandom patterns in genomic sequences related to viral DNA replication and gene expression.

Jorge Villalobos - The Civil Engineering Laboratory of Advanced Dynamic Traffic and Urban Systems (LADTUS) are currently collaborating with the UTEP Math Department through the use of Felina. LADTUS is developing a Parallel Traffic Simulation and Dynamic Traffic Assignment tool for use in Transportation Infrastructure planning and Evacuation planning and system dynamics modeling of critical infrastructure.

Rajendra Zope - The objective is to design computationally efficient method for electronic structure calculations of large molecules like fullerenes, quantum dots, nanostructured materials. The platform will be used to develop and test the ADFT code and also for its applications to systems mentioned above. Recently, using ADFT that is parametrized to give exact geometry of the C60 fullerene, we fully optimized carbon fullerene containing more than two thousand atoms (C2160) at the all electron level and using triple zeta quality (6-311G**) basis set (total 39000 basis functions).

EXAMPLE: Fully optimized fullerenes.