Space-Time Multiscale Model for Wave Propagation in Heterogeneous Media
نویسندگان
چکیده
Abstract: A space-time multiscale model for wave propagation in heterogeneous media is developed. The model builds on the authors’ previous work on the higher-order mathematical homogenization theory with multiple spatial and temporal scales, and is aimed at addressing the issues of stability and mathematical consistency. Starting from the weak forms of homogenized macroscopic equations of motion, terms causing the solution secularity are identified and enforced to vanish. This condition recovers the missing boundary conditions and gives rise to two secularity constrains imposing the uniform validity of asymptotic expansions. Finite element semidiscretization in space along with an analytical solution in time are employed to incorporate the secularity constrains in the leading-order solution and account for the slow time dependence of the leading solution. Pade approximation is utilized to develop the time stepping schemes on the fast time scale. The formulation is verified for wave propagation problems in semi-infinite and finite domains.
منابع مشابه
Analysis of Heterogeneous Multiscale Methods for Long Time Wave Propagation Problems
In this paper, we analyze a multiscale method developed under the heterogeneous multiscale method (HMM) framework for numerical approximation of multiscale wave propagation problems in periodic media. In particular, we are interested in the long time O(ε−2) wave propagation, where ε represents the size of the microscopic variations in the media. In large time scales, the solutions of multiscale...
متن کاملکاربرد روش معادله سهموی در تحلیل مسائل انتشار امواج داخل ساختمان
With the rapid growth of indoor wireless communication systems, the need to accurately model radio wave propagation inside the building environments has increased. Many site-specific methods have been proposed for modeling indoor radio channels. Among these methods, the ray tracing algorithm and the finite-difference time domain (FDTD) method are the most popular ones. The ray tracing approach ...
متن کاملTorsional Surface Wave Propagation in Anisotropic Layer Sandwiched Between Heterogeneous Half-Space
The present paper studies the possibility of propagation of torsional surface waves in an inhomogeneous anisotropic layer lying between two heterogeneous half-spaces (upper and lower half-space). Both the half-spaces are assumed to be under compressive initial stress. The study reveals that under the assumed conditions, a torsional surface wave propagates in the medium. The dispersion relation ...
متن کاملMultiscale Methods for Wave Propagation in Heterogeneous Media Over Long Time
Multiscale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods for multiscale wave propagation in the framework of the heterogeneous multiscale method (HMM). The numerical methods couple simulation...
متن کاملLove Wave Propagation in a Fiber-reinforced Layer with Corrugated Boundaries Overlying Heterogeneous Half-space
Love-type wave generation in a fiber-reinforced medium placed over an inhomogeneous orthotropic half-space is analysed. The upper and lower boundary surfaces of the fiber reinforced medium are periodically corrugated. Inhomogeneity of half-space is caused by variable density and variable shear modules. Displacement components for layer and half-space are derived by applying separable variable t...
متن کامل