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Research Interests
- Numerical linear algebra and matrix computations
- Model order reduction techniques for various analysis
(steady-state, transient analysis, sensitivity analysis) of
large-scale dynamical systems and
its applications. In particular, structure-persevering and
substructuring methods.
- Linear and nonlinear (large-scale) eigenvalue problems
- Parallel scientific computing
Research Projects
- Substructuring methods I -
mode selection criterion
(with Z. Bai)
Substructuring methods have been studied in structural dynamics
analysis since 1960s.
Main attraction points of substructuring methods are
exploiting underlying structures of a system explicitly,
avoiding the expenses of processing the entire system at once,
able to be conducted in parallel, and
preserving the structure of subsystems.
These features enable substructuring methods to tackle very
large problems efficiently.
However, in these substructure-based methods, the modes of
subsystems associated with the lowest frequencies are typically
retained.
This mode selection rule is largely heuristic.
We work on deriving mode selection rules and their associated
theories.
We have derived a sub-optimal selection rule by using
moment-matching analysis for one-level substructuring method.
(We called
CMSχ
-- An alternative mode selection to the Component Mode Synthesis
(CMS) methods.) We continue working on better mode selection rules
and its multilevel extension.
Papers and Presentations:
- B.-S. Liao, Z. Bai and W. Gao, The important modes of
subsystems: a moment-matching approach. Accepted by
International Journal for Numerical Methods in Engineering
, 2006.
- (Sub)optimal mode selection for modal reduction of subsystems,
(with Z. Bai - presenter).
SIAM Annual Meeting, Jul 2005.
- Optimal Mode Selection for Substructuring Method.
Poster presentation at Bay Area Scientific Computing Day,
Mar 2005.
- Z. Bai and B.-S. Liao,
Towards an Optimal Substructuring Method for Model Reduction.
Springer Lecture Notes in Computer Science Vol 3732,
pp. 276-285, 2006.
(pdf file)
- Substructuring method for system-on-chip simulation.
Meeting talk given at UC Davis with
Synopsys
researchers, Dec 2004.
- Substructuring methods II -
Krylov subspace basis
(with Z. Bai)
This is continued work from above project.
We observe that modal reduction methods (including multilevel
substructuring methods) are generally less accurate and
efficient than Krylov subspace-based reduction methods.
We investigate how to replace eigenbases by Krylov subspace
bases (including multilevel extensions).
This type method is appealing since it not only takes the
advantages of substructuring methods (parallel-computing,
structure-persevering, ...) but also improves the
accuracy by using the Krylov subspace bases.
Papers and Presentations:
Presentations for substructuring methods
(combination of I and II):
- What are good bases of substructures for substructuring methods?
Colloquial talk given in at National Central University,
Taiwan, Dec 2005.
- What are good bases of substructures for substructuring methods?
Colloquial talk given in at Tamkang University, Taiwan,
Dec 2005.
- Large-scale nonlinear eigensolvers
(with Z. Bai, L. Lee, and K. Ko)
(I was a visiting researcher in Advanced Computations
Department
(ACD)
at Stanford Linear Accelerator Center
(SLAC)
where I worked on developing nonlinear eigensolvers for accelerator
RF cavity modeling during the Summer 2005)
Recently, large-scale nonlinear eigensolvers have been attracted
a lot of attention. Partly reason is that modeling real world
eigenproblems generally results in certain type nonlinearity.
For example, dynamic analysis of vibration and non-proportional
damping of a structure and modeling RF cavity design.
The fundamental difficulty is that nonlinearity can be very
complicated and the problems are large. A straightforward
Newton's type method is not feasible. We work on developing robust
and efficient subspace-type methods and their associated theories
for (at least) certain type nonlinear eigenproblems
(hopefully, can apply to many different applications).
Papers and Presentations:
- An iterative projection method for solving large-scale
nonlinear
eigenvalue problems with application to next-generation
accelerator design. Invited talk given at Ninth Copper Mountain
Conference on Iterative Methods, Apr 2006.
- Numerical methods for large-scale electromagnetic application.
Seminar talk given at National Center of Theoretical Science,
Taiwan, Dec 2005.
- Numerical methods for nonlinear eigenproblems in RF cavity
design. Seminar talk given at SLAC, Sep 2005.
- Solving nonlinear eigenproblems in Accelerator cavity design,
(with L. Lee - presenter, SLAC team, Z.Bai and LBL team).
SIAM Annual Meeting, Jul 2005.
- Fast linear solvers for large-scale sequential
low-rank modified linear systems
(with J. E. Bolander)
This work is inspired by fracture simulation. In the fracture
simulation, solving several thousands of large-scale
successive low-rank-modified linear systems is needed.
(See the fracture process
here and
image gallery at J.E. Bolander homepage).
We successfully used the low-rank update process to have about
two orders of magnitude computational time less than the ordinary
direct sparse solver to complete a fracture cycle.
One typical example is that a seven
day computing work now only needs about 10 hours.
We continue working on other possible fast solvers such as PCG
method.
Papers and Presentations:
- M. Yip, Z. Li, B.-S. Liao, and J. E. Bolander,
Irregular lattice models
of fracture of multiphase particulate materials.
Accepted by International Journal of Fracture, 2006.
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