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Regularization of B-Spline Objects
Spline objects Regularization L2-gradient Finite element method
2012/8/8
By a d-dimensional B-spline object (denoted as Od), we mean a B-spline curve (d = 1), a
B-spline surface (d = 2) or a B-spline volume (d = 3). By regularization of a B-spline object
Od we mean a pro...
An Explicit Harmonic Extension for the Constant-like Basis and Its Application to Domain Decompositions
domain decomposition coarse subspace constant-like basis nearly harmonic extension preconditioner inexact solvers condition number
2012/8/8
In this paper we are concerned with substructuring methods for the second-order
elliptic problems in three-dimensional domains. We 痳st design a simple and completely
explicit nearly harmonic extensi...
Cascadic Multigrid Methods For Parabolic Problems
Cascadic multigrid method parabolic problem element methods backwardEuler scheme smoother stability optimal error order optimal complexity
2012/8/8
In this paper, we consider the cascadic multigrid method for a parabolic type equa-
tion. Backward Euler approximation in time and linear 痭ite element approximation in space are
employed. A stabilit...
A Non-overlapping Domain Decomposition Method with Inexact Solvers
domain decomposition interface space multilevel decomposition constant-like function nearly harmonic extension preconditioner inexact solvers condition number
2012/8/8
In this paper we are concerned with non-overlapping domain decomposition methods
for the second-order elliptic problems in three-dimensional domains. We develop a
new kind of substructuring method, ...
Consistent Approximations of Some Geometric Differential Operators and Their Convergences
Geometric Di erential Operators Consistent discretized approximations TriangularKey words:Surface Mesh Error Analysis
2012/8/8
The numerical integration of many geometric partial di erential equations involves
discrete approximations of several first- and second-order geometric di erential operators.
In this paper, we consi...
Energy-conserving numerical methods for multi-symplectic Hamiltonian PDEs
Energy-conserving numerical methods Hamiltonian PDEs
2012/8/8
In this paper, the discrete gradient methods are investigated for ODEs with 痳st integral,
and the recursive formula is presented for deriving the high-order numerical methods. We
generalize the idea...
A generalized Peierls-Nabarro model for curved dislocations and core structures of dislocation loops in Al and Cu
Dislocation dislocation structures micromechanical modeling Peierls-Nabarro model
2012/8/8
In this paper, we present a generalized Peierls-Nabarro model for curved dislo-
cations. In the generalized Peierls-Nabarro model, the anisotropic elastic energy is
obtained e±ciently by solving the...
An Adaptive Uniaxial Perfectly Matched Layer Method For Time-Harmonic Scattering Problems
Adaptivity uniaxial perfectly matched layer a posteriori error analysis acousticscattering problems
2012/8/8
The uniaxial perfectly matched layer (PML) method uses rectangular domain to
define the PML problem and thus provides greater flexibility and efficiency in dealing with prob-
lems involving anisotro...
An Adaptive Uniaxial Perfectly Matched Layer Method For Time-Harmonic Scattering Problems
Adaptivity uniaxial perfectly matched layer a posteriori error analysis acousticscattering problems
2012/8/8
The uniaxial perfectly matched layer (PML) method uses rectangular domain to
define the PML problem and thus provides greater flexibility and efficiency in dealing with prob-
lems involving anisotro...
New type of KP equation with self-consistent sources and its bilinear B鋍klund transformation
New type of KP equation self-consistent
2012/8/8
A new type of the KP equation with self-consistent sources (KPESCS)
痳st found by Melnikov ( Lett. Math. Phys. 7(1983) 129-136)is re-constructed
via source generation procedure. New feature of the ob...
A Discrete Weighted Helmholtz Decomposition and Applications to Non-overlapping Domain Decomposition for Saddle-point Maxwell Systems with Jumps in Coefficients
Maxwell's equations N秂d秂lec 痭ite elements weighted Helmholtz decom-position domain decomposition saddle-point system, preconditioners, condition number
2012/8/8
We shall establish a discrete weighted Helmholtz decomposition in edge element
spaces, which is stable uniformly with respect to the jumps in the discontinuous weight
function. The stable decomposit...
A Local Computational Scheme for Higher Order Finite Element Eigenvalue Approximations
Eigenvalue 痭 ite element higher order local computation
2012/8/8
Based on some coupled discretizations, a local computational scheme is proposed
and analyzed in this paper for a class of higher order 痭ite element eigenvalue approximations. Its
e眂iency is proven b...
Construction of exact invariants of time-dependent linear nonholonomic dynamical systems
invariant Lie algebraic method linear nonholonomic Hamiltonian system
2012/8/8
In this work, we build exact dynamical invariants for time-dependent, linear, nonholo-
nomic Hamiltonian systems in two dimensions. Our aim is to obtain an additional insight into
the theoretical un...