The Finite Element Numerical Method Of 3-D Nonlinear Primary Wave Equation In Isotropy Elastic Solid Medium

The research of the nonlinear theory is the science on the complexity. Nonlinear waveis an important part of it. Recently, the propagation has become more and more importantin a large number of fields of physics and engineering science。The earth is a complicatedand changing system, so there have complexity and nonlinear, we can't get all data fromearthquakes. How to find the biggest degree to use these data and improve dependability,so as to embody great economical benefit in searching now oil fields, it's necessary for usto study the nonlinear wave.The 3-D nonlinear longitudinal wave in the isotropy solid medium studied in this paperis the finite amplitude wave, which thought about the nonlinear of the motion and med-ium. The finite element numerical method based on centimo theory and dispart-insert-value One side, it is conventional energy method. It is transfiguration of Ritz-Galerkinmethod .On the other hand, it also has some similitude with difference method Therefore,the finite element numerical method is the unite of energy method and difference method.The finite element disperse keep the symmetry poditive nature of original problem. Evenits freshness matrix is sparsity matrix. All of these excellence make numerical value com-pute easy. But wave energy look toward to high frequency space, these lead to strong dis-sipation in the high frequency, accelerating the nonlinear wave dissipation. In this time,the nonlinear is the mainly characteristic, so we reasonable analyze the medium nonlinearaction is most necessary. The finite element method is made use of the nonlinear waveequations, along with increment of degree of freedom in unit , the precision of interpo-lateing function and approximate solution have to certain extent difficulty .Every concretenonlinear wave equation need concrete interpolating function, variant periphery conditionneed variant precise approximate function. We can put to use variant approximate functionin variant unit. We can utilize variant interpolating function in variant periphery condition.By this method, we can heighten precision and quicken the velocity of convergence.We gained the solution of hyperbolic 3-D nonlinear primary wave equation by finiteelement numerical method .Based on the proof of existence of the exact value , we havegained the numerical value, analyzed the stability, convergence, and established the errorestimate formula.Firstly, the basic theory of nonlinear science was introduced and its influences on thedevelopment of science and technology were showed in this paper. Furthermore, thehistory and its modern status of solutions on non-linear wave equations were shown here.Secondly, in this paper, Physical and mathematical fundamental of the nonlinear waveis introduced, especially, with regard to the nonlinear wave of elastic solid medium. Formof point of view, the conception of the strain work is introduced. We built 3-D hyperbolicnonlinear evolution and the general motion equation by making good use of the cons-ervation of mass,moment and energy. Meanwhile, the paper builds three-dimensionnonlinear wave model in isotropic medium.Lastly, existence of the exact value have been rigidly proved with functional analysis.Based on it , we have gained the numerical value,analyzed the stability,convergence, andestablished the error estimate formula. this paper studies the mathematical theories of thefinite element numerical method and the nonlinear functional analysis's basic theory,introducing the process and the procedure plan of the finite element method and thedouble grid method for the nonlinear equations. In these theories, Ignoring the transversewave domino effect, 3-D nonlinear Primary wave equation in isotropy solid medium wasgained. and we fetch the constant about the elliptical projection operator, and completethe nonlinear primary wave of the half disperse finite element numerical result's errorestimate and the nonlinear primary-transverse wave of half disperse finite elementnumerical result's error estimate in the Sobolev space, further, we obtain theexistence,convergence ,stability and error estimate of the whole disperse finite elementmethod. In the following of these, we solve the kind of the nonlinear Primary-transversewave equations by using of the finite method, analyzing the transmitted essence of thenonlinear Primary-transverse wave by the use of graph. In the process of simulation, wesynthesis apply the trick of numerical integral,interpose value, the procedure design.While solving the nonlinear wave equations, the finite element numerical method holdsthe excellency of classicality Ritz-Galerkin method by constructing radicle function offinite dimension space SN with dissect and insert value, at the same time, it also conquerits deficiency. This method is especially the same with region ? ,which with complexshape ,the fix dispel term containing the second or the third boundary term ,and themodulus of the equations is disconnected .The nonlinear wave is more and more important in the applied earthquake prospect, thenonlinear action of medium shows further adding frequency, and the reason of thenonlinear effected the reducing and scattering of wave, new high frequency wave iseasier to scatter and attenuation, but wave energy look toward to high frequency space,these lead to strong dissipation in the high frequency, accelerating the nonlinear wavedissipation. In this time, the nonlinear is the mainly characteristic, so we reasonableanalyze the medium nonlinear action is most necessary. The finite element method ismade use of the nonlinear wave equations, along with increment of degree of freedom inunit, the precision of interpolating function and approximate solution have to certainextent difficulty. Every concrete nonlinear wave equation need concrete interpolatingfunction, variant periphery condition need variant precise approximate function. We canput to use variant approximate function in variant unit. We can utilize variantinterpolating function in variant periphery condition. By this method, we can heightenprecision and quicken the velocity of convergence.To the two degree and more high degree and more complexity situation, no matter whatnumerical result or analytic result, all are most difficult. We gained the solution ofhyperbolic 3-D nonlinear primary wave and it's transmitting, in order to practicalappliance, the third degree the nonlinear wave of research are most necessary andimportant.