Research
Advanced numerical simulation and analysis
for structures, fluids, heat transfer, and their interaction. Applications
include acoustic radiation and
scattering from submerged elastic structures
including submarines and other marine structures, scattering from electromagnetic
devices, and acoustic focusing for biomedical applications.
Structural acoustics and vibration is the study of how sound and mechanical
structures interact; for example, the transmission of sound through walls
and the radiation of sound from vehicle panels.
Basic discretization
methodologies, including treatment of exterior domains through hybrid analytical/numerical
methods, treatment of structural complexity, unstructured and adaptive
finite element technology,
iterative methods for large-scale computer
simulations on distributed memory parallel processor architectures,
and high-performance computing. For
problems in unbounded domains, nonreflecting boundary conditions
and infinite elements which eliminate or minimize reflection of outgoing
waves are developed. Inverse scattering methods are also developed.
Examples Link
Space-Time Discontinuous Galerkin Methods:
Development of reliable and
accurate space-time finite element methods for transient wave propagation
in solids/structure and acoustic fluids. High-order accurate approximations
are made in both space and time. Efficient iterative solution methods
are developed for distributed memory parallel computers.
Optimal error estimates using functional analysis
are predicted and confirmed numerically in large-scale simulations. Development
of efficient and accurate local error indicators to drive the implementation
of adaptive mesh refinement/unrefinement strategies for static and dynamic
analysis of structures and fluids.
Adaptive space-time finite elements automatically refines
itself to maintain adequate spatial and temporal resolution
in select regions. Applying this algorithm to a simulation of structural
acoustics, we use adaptive-mesh refinement to achieve very high spatial
and temporal dynamic range in regions where wave fronts are forming while we
make do with much lower resolution in quiscent regions where very little
structure is present. An equivalent calculation using traditional
semi-discrete time-integration methods would
require significantly more processing time and memory usage.
Parallel Iterative Methods for Acoustic Scattering with Exact
Nonreflecting Boundaries
Numerical solutions for acoustic radiation and scattering problems in unbounded domains
require a large number of element unknowns to resolve high wavenumber/frequency problems.
To solve these problems efficiently on today's computer architectures,
it is required to distribute the work and memory on multi-processors and compute
in parallel.
Parallel iterative methods for fast solution of large-scale acoustic
radiation and scattering problems are developed using
exact Dirichlet-to-Neumann (DtN) nonreflecting boundaries.
A separable elliptic nonreflecting boundary is used to
efficiently model unbounded regions surrounding elongated structures.
We exploit the special structure of the non-local DtN map as a low-rank update
of the system matrix to efficiently compute the matrix-by-vector products
found in Krylov subspace based iterative methods.
We develop distributed-memory parallel
iterative methods in conjunction with parallel algebraic preconditioners.
Domain decomposition with interface minimization is performed to ensure
optimal inter-processor communication. Implementations use
the Single Program Multiple Data (SPMD) model with MPI.
We demonstrate that with clever implementations,
the non-local character of the DtN map
does not significantly decrease the scale up and
parallel efficiency versus a purely approximate local boundary condition.
Residual Based Methods for Structures, Acoustics, and their Interaction:
Development
of stabilized finite element methods for the dynamic response
of plates, shells and their interaction with acoustic fluids. Complex wavenumber dispersion
analysis is used to provide criteria for the design of optimal finite element
models for wave propagation in elastic and acoustic media. High-order finite
and spectral element methods are developed to reduce numerical dispersion.
Signal processing techniques including Fast-Fourier and Wavelet transforms,
and high-resolution parameter estimation schemes are used to obtain critical
design values.
Meshless methods:
Development of
meshless computational methods for wave propagation in
acoustics, structures, and their interaction. Meshless methods
eliminate the need for complicated element connectivity data
in complex three-dimensional problems. The basis functions generated
in these meshless methods allow for high accurate phase and
amplitude response for wave propagation phenomena.
Plate and Shell Finite Elements:
Finite elements for laminated
composites where interlaminar stresses are of interest. Use of high-order
hp-version and spectral finite elements for plates and shells. Development
of accurate and efficient shell finite elements with drilling degrees of
freedom for nonlinear structural dynamics. Numerical modelling of piezoceramics
and viscoelastic composites, including fiber/matrix interaction.
Design and Optimization of Automotive Systems:
Design and analysis of vehicle
suspension and chassis coupled with full finite element models
of body-in-white structure
under steady-state and dynamic conditions. Techniques include
adaptive meshing, shape and geometric optimization.
Adaptive and optimization techniques are also used to design
suspension components for increased strength and minimum weight.
Lightweight Automotive Engineering:
Reverse Engineering of automotive systems.
Finite element modeling and analysis tools enable in-depth understanding
and redesign for high-impact crash.
Both evolutionary and revolutionary new concepts and
detailed design. Integrated design including
material selection, topology optimization, manufacuring
processes, load analysis. The lightweight technology developed by
Clemson reduces weight, and improves handling and fuel economy.
-L.L.Thompson
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