In this paper, we introduce two novel split weighted least-squares finite element procedures for pseudo-hyperbolic equations arising in the modelling of nerve conduction process. By selecting the ...weighted least-squares functional properly, each procedure can be split into two independent symmetric positive definite sub-procedures. One of sub-procedures is for the primitive unknown variable, which is the same as the standard Galerkin finite element procedure and the other is for the introduced flux variable. Optimal order error estimates are developed and the numerical example is given to show the efficiency of the introduced schemes.
We study a model of continuous sedimentation. Under idealizing assumptions, the settling of the solid particles under the influence of gravity can be described by the initial value problem for a ...one-dimensional scalar conservation law with a flux function that depends discontinuously on the spatial position. We construct a weak solution to the sedimentation model by proving the convergence of a front tracking method. The basic building block in this method is the solution of the Riemann problem, which is complicated by the fact that the flux function is discontinuous. A feature of the convergence analysis is the difficulty of bounding the total variation of the conserved variable. To overcome this obstacle, we rely on a certain non-linear Temple functional under which the total variation can be bounded. The total variation bound on the transformed variable also implies that the front tracking construction is well defined. Finally, via some numerical examples, we demonstrate that the front tracking method can be used as a highly efficient and accurate simulation tool for continuous sedimentation.
The Delft approach, a method for the deformation analysis, is presented in this article. Based on geodetic measurements, the statistical significance of displacements at the surface is determined ...with statistical methods. A numerical example shows the effectiveness of the presented method.
In this paper, we introduce a Crank-Nicolson split least-squares Galerkin finite element procedure for parabolic integro-differential equations, arising in the modeling of nonlocal reactive flows in ...porous media. By selecting the least-squares functional properly, the procedure can be split into two independent sub-procedures, one of which is for the primitive unknown and the other is for the flux. By carefully choosing projections, we get optimal order
H
1
(
Ω
) and
L
2
(
Ω
) norm error estimates for
u
and sub-optimal (
L
2
(
Ω
))
d
norm error estimate for
σ
with second-order accuracy in time increment. The numerical examples are given to testify the efficiency of the introduced scheme.
For ant colony algorithm to search for a long time, easy to occur Stagnant phenomenon and sink into local most superior defects, and puts forward a kind of immune mechanism of the ant colony ...algorithm, and the algorithm is applied to typical water supply network in the combinatorial optimization problem. Combined with water supply network for example problem using respectively based on immune mechanisms of the ant colony algorithm and genetic algorithm and the basic ant colony algorithm for example to analysis. The results show that the improved algorithm is easier to realize the global optimal solution, and high efficiency, the optimization algorithm is better than other traditional optimization for solving water distribution network ability. So demonstrate the effectiveness of the algorithm.
Two least-squares Galerkin finite element schemes are formulated to solve pseudohyperbolic equations. The advantage of this method is that it is not subject to the LBB condition. The convergence ...analysis shows that the methods both yield the approximate solutions with optimal accuracy in
(
L
2
(
Ω
)
)
2
×
L
2
(
Ω
)
. Moreover, the two methods get the approximate solutions with first-order and second-order accuracy in time increment, respectively. Numerical example shows that the two schemes are effective.
In this paper, we introduce two split least-squares Galerkin finite element procedures for pseudohyperbolic equations arising in the modelling of nerve conduction process. By selecting the ...least-squares functional properly, the procedures can be split into two sub-procedures, one of which is for the primitive unknown variable and the other is for the flux. The convergence analysis shows that both the two methods yield the approximate solutions with optimal accuracy in
L
2
(
Ω
)
norm for
u
and
u
t
and
(
L
2
(
Ω
)
)
2
norm for the flux
σ
. Moreover, the two methods get approximate solutions with first-order and second-order accuracy in time increment, respectively. A numerical example is given to show the efficiency of the introduced schemes.
In this paper, we suggest and analyze a new iterative method for finding approximate solution of the nonlinear equation
f(
x)
=
0. It is shown that proposed method has fourth-order convergence. ...Several numerical examples are given to illustrate that the method developed in this paper give better results than the other methods including Newton method.
The problem of robust training sequence design for the purpose of multiple-input multiple-output (MIMO) channel estimation is considered. In particular, we aim to minimize the worst-case mean squared ...error of the channel estimates which is formulated as a minimax optimization problem. This problem is addressed efficiently using an extended barrier method under the general assumption of an arbitrary compact convex uncertainty set. Moreover, assuming a Kronecker MIMO channel and a unitarily invariant uncertainty set, the robust design problem is diagonalized which significantly lowers the dimensionality of the optimization problem. We provide numerical examples to illustrate the performance of the proposed design.
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