233 research outputs found
A meshless method for an inverse two-phase one-dimensional nonlinear Stefan problem
We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase inverse linear Stefan problem, to the nonlinear case. In this latter situation the free surface is also considered unknown which is more realistic from the practical point of view. Building on the earlier work, the solution is approximated in each phase by a linear combination of fundamental solutions to the heat equation. The implementation and analysis are more complicated in the present situation since one needs to deal with a nonlinear minimization problem to identify the free surface. Furthermore, the inverse problem is ill-posed since small errors in the input measured data can cause large deviations in the desired solution. Therefore, regularization needs to be incorporated in the objective function which is minimized in order to obtain a stable solution. Numerical results are presented and discussed
Collocation Method using Compactly Supported Radial Basis Function for Solving Volterra's Population Model
In this paper, indirect collocation approach based on compactly supported
radial basis function is applied for solving Volterras population model. The
method reduces the solution of this problem to the solution of a system of
algebraic equations. Volterras model is a non-linear integro-differential
equation where the integral term represents the effect of toxin. To solve the
problem, we use the well-known CSRBF: Wendland3,5. Numerical results and
residual norm 2 show good accuracy and rate of convergence.Comment: 8 pages , 1 figure. arXiv admin note: text overlap with
arXiv:1008.233
The method of fundamental solutions for some direct and inverse problems
We propose and investigate applications of the method of fundamental solutions (MFS) to several parabolic time-dependent direct and inverse heat conduction problems (IHCP). In particular, the two-dimensional heat conduction problem, the backward heat conduction problem (BHCP), the two-dimensional Cauchy problem, radially symmetric and axisymmetric BHCPs, the radially symmetric IHCP, inverse one and two-phase linear Stefan problems, the inverse Cauchy-Stefan problem, and the inverse two-phase one-dimensional nonlinear Stefan problem. The MFS is a collocation method therefore it does not require mesh generation or integration over the solution boundary, making it suitable for solving inverse problems, like the BHCP, an ill-posed problem. We extend the MFS proposed in Johansson and Lesnic (2008) for the direct one-dimensional heat equation, and Johansson and Lesnic (2009) for the direct one-phase one-dimensional Stefan problem, with source points placed outside the space domain of interest and in time. Theoretical properties, including linear independence and denseness, the placement of source points, and numerical investigations are included showing that accurate results can be efficiently obtained with small computational cost. Regularization techniques, in particular, Tikhonov regularization, in conjunction with the L-curve criterion, are used to solve the illconditioned systems generated by this method. In Chapters 6 and 8, investigating the linear and nonlinear Stefan problems, the MATLAB toolbox lsqnonlin, which is designed to minimize a sum of squares, is used
Software for evaluating probability-based integrity of reinforced concrete structures
In recent years, much research work has been carried out in order to obtain a more
controlled durability and long-term performance of concrete structures in chloride containing environment. In particular, the development of new procedures for
probability-based durability design has proved to give a more realistic basis for the
analysis. Although there is still a lack of relevant data, this approach has been
successfully applied to several new concrete structures, where requirements to a more controlled durability and service life have been specified. A probability-based durability analysis has also become an important and integral part of condition assessment of existing concrete structures in chloride containing environment. In order to facilitate the probability-based durability analysis, a software named DURACON has been developed, where the probabilistic approach is based on a Monte Carlo simulation. In the present paper, the software for the probability-based durability analysis is briefly described and used in order to demonstrate the importance of the various durability parameters affecting the durability of concrete structures in chloride containing environment
SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES
Crack propagation in thin shell structures due to cutting is conveniently simulated
using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell
elements are usually preferred for the discretization in the presence of complex material
behavior and degradation phenomena such as delamination, since they allow for a correct
representation of the thickness geometry. However, in solid-shell elements the small thickness
leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new
selective mass scaling technique is proposed to increase the time-step size without affecting
accuracy. New âdirectionalâ cohesive interface elements are used in conjunction with selective
mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile
shells
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Schnelle Löser fĂŒr partielle Differentialgleichungen
The workshop Schnelle LoÌser fuÌr partielle Differentialgleichungen, organised by Randolph E. Bank (La Jolla), Wolfgang Hackbusch(Leipzig), Gabriel Wittum (Heidelberg) was held May 22nd - May 28th, 2005. This meeting was well attended by 47 participants with broad geographic representation from 9 countries and 3 continents. This workshop was a nice blend of researchers with various backgrounds
Determination of a Time-Dependent Free Boundary in a Two-Dimensional Parabolic Problem
The retrieval of the timewise-dependent intensity of a free boundary and the temperature in a two-dimensional parabolic problem is, for the first time, numerically solved. The measurement, which is sufficient to provide a unique solution, consists of the mass/energy of the thermal system. A stability theorem is proved based on the Green function theory and Volterraâs integral equations of the second kind. The resulting nonlinear minimization is numerically solved using the lsqnonlin MATLAB optimization routine. The results illustrate the reliability, in terms of accuracy and stability, of the time-dependent free surface reconstruction
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