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An original signal processing method called delayed Time Reversal-Nonlinear Elastic Wave Spectroscopy is introduced in the present paper. The method could be used to amplify signal in certain regions of the material under Non Destructive Testing. It allows to optimize and change the shape of the received focused wave in the material, either by making the focusing sharper by decreasing the side lobes or making it wider by modifying the actual focusing peak. It is also possible to use the focused signal as a delta-basis to construct a signal with arbitrary envelope or reduce the side lobes of the focused signal. These concepts are shown to work well in the simulations and the physical experiments. This signal processing method is particularly promising for nonlinear and solitary wave analysis, since it allows to create an interaction of sharp and solitary wave peaks just underneath the receiving transducer. Due to simple and accurate linear prediction of the received interaction signal, any differences of measurements and predictions could indicate the presence of nonlinearities. [ABSTRACT FROM AUTHOR]

This paper is devoted to the valuation of American multi-asset put options. It is well known that the American multi-asset put option satisfies a linear complementary problem (LCP) on an unbounded domain. We consider a penalty method in which the LCP could be reformulated into a nonlinear parabolic problem on an unbounded domain. For the unbounded computational domain, a perfectly matched layer (PML) technique is applied to truncate it. As to the resulting bounded domain problem related to the option, we use a semi-implicit finite element method (SIFEM) to solve it. The convergence of this method is analyzed in detail. Finally, we present some numerical simulations to show the validity and efficiency of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Abstract: The traditional scaled boundary finite-element method (SBFEM) is a rather efficient semi-analytical technique widely applied in engineering, which is however valid mostly for linear differential equations. In this paper, the traditional SBFEM is combined with the homotopy analysis method (HAM), an analytic technique for strongly nonlinear problems: a nonlinear equation is first transformed into a series of linear equations by means of the HAM, and then solved by the traditional SBFEM. In this way, the traditional SBFEM is extended to nonlinear differential equations. A nonlinear heat transfer problem is used as an example to show the validity and computational efficiency of this new SBFEM. [ABSTRACT FROM AUTHOR]