## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

DCDS-B

We prove that a polygonal scatterer in $\mathbb{R}^2$, possibly
consisting of finitely many sound-soft and sound-hard polygons, is
uniquely determined by a single far-field measurement.

IPI

We investigate a qualitative method for imaging acoustic obstacles
in two and three dimensions by boundary measurements corresponding to
hypersingular point sources. Rigorous
mathematical justification of the imaging method is established, and
numerical experiments are presented to illustrate the effectiveness
of the proposed imaging scheme.

DCDS-B

This work is concerned with the finite element solutions for
parameter identifications in second order elliptic and parabolic
systems. The $L^2$- and energy-norm error estimates of the finite
element solutions are established in terms of the mesh size, time
step size, regularization parameter and noise level.

IPI

This work is concerned with a direct sampling method (DSM)
for inverse acoustic scattering problems using far-field data.
Using one or few incident waves, the DSM provides quite
reasonable profiles of scatterers in time-harmonic inverse acoustic
scattering without a priori knowledge of either the physical properties
or the number of disconnected components of the scatterer. We shall
first present a novel derivation of the DSM using far-field data,
then carry out a systematic evaluation of the performances and distinctions
of the DSM using both near-field and far-field data. A new
interpretation from the physical perspective is provided based on some
numerical observations.
It is shown from a variety of numerical experiments that the method
has several interesting and promising potentials:
a) ability to identify not only medium scatterers, but also obstacles,
and even cracks, using measurement data from one or few incident directions,
b) robustness with respect to large noise, and c) computational efficiency
with only inner products involved.

IPI

In 2012, there were two scientific conferences in honor of Professor Tony
F. Chan's 60th birthday. The first one was ``The
International Conference on Scientific Computing'', which took place
in Hong Kong from January 4-7. The second one, ``The International
Conference on the Frontier of Computational and Applied Mathematics'',
was held at the Institute of Pure and Applied Mathematics (IPAM) of
UCLA from June 8-10. Invitations were also sent out to conference speakers,
participants, Professor Chan's former colleagues, collaborators and
students, to solicit for original research papers. After the
standard peer review processes, we have collected 23 papers in this special
issue dedicated to Professor Chan to celebrate his contribution
and leadership in the area of scientific computing and image
processing.

For more information please click the “Full Text” above.

For more information please click the “Full Text” above.

keywords:

DCDS-B

We present some new a priori estimates of the solutions to three-dimensional
elliptic interface problems and static Maxwell interface system with variable
coefficients. Different from the classical a priori estimates, the physical
coefficients of the interface problems appear in these new estimates
explicitly.

DCDS

In this paper we study a degenerate evolution system
$\mathbf H_t +\nabla \times [|\nabla \times \mathbf H|^{p-2}\nabla \times \mathbf H]=\mathbf F$ in a bounded domain as well as its limit as $p\to \infty$ subject
to appropriate initial and boundary conditions. This system governs the evolution
of the magnetic field $\mathbf H$ in a conductive medium under the influence of a system
force $\mathbf F$. The system is an approximation of Bean's critical-state model for type-II superconductors. The existence, uniqueness and regularity of solutions to the
system are established. Moreover, it is shown that the limit of $\mathbf H(x, t)$ as $p\to \infty$
is a solution to the Bean model.

IPI

We shall derive and propose several efficient
overlapping domain decomposition methods for solving some typical
linear inverse problems, including the identification of the flux,
the source strength and the initial temperature in
second order elliptic and parabolic systems. The methods are iterative, and
computationally very efficient: only local forward and adjoint problems
need to be solved in each subdomain, and the local minimizations have
explicit solutions.
Numerical experiments are provided to demonstrate the robustness and efficiency
of the methods: the algorithms
converge globally, even with rather poor initial guesses;
and their convergences do not deteriorate or deteriorate
only slightly when the meshes are refined.

CPAA

In this paper, we address an inverse problem of reconstruction of
the initial temperature in a heat conductive system when some
measurement data of temperature
are available, which may be observed in a subregion
inside or on the boundary of the physical domain, along a time
period which may start at some point, possibly far away from the
initial time. A conditional stability estimate is first achieved by
the Carleman estimate for such reconstruction. Numerical
reconstruction algorithm is proposed based on the output
least-squares formulation with the Tikhonov regularization using the
finite element discretization, and the existence and convergence of
the finite element solution are presented. Numerical experiments are
carried out to demonstrate the applicability and effectiveness of
the proposed method.

IPI

In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady
source identification problem governed by the linear convection-diffusion equation.
Traditional approaches require to solve repeatedly a forward parabolic system, an adjoint system and a
system with respect to the unknown sources.
The three systems have to be solved one after another.
These sequential steps are not desirable for large scale parallel computing.
A space-time restrictive additive Schwarz method is proposed for a fully implicit space-time coupled discretization scheme
to recover the time-dependent pollutant source intensity functions.
We show with numerical experiments that the scheme works well with noise in the observation data.
More importantly it is demonstrated that the parallel space-time Schwarz preconditioner is scalable on a supercomputer with over $10^3$ processors,
thus promising for large scale applications.

## Year of publication

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