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Quadrature formulas for integration of multivariate trigonometric polynomials on spherical triangles
Springer Science and Business Media LLC - Tập 3 - Trang 119-138 - 2012
J. Beckmann, H. N. Mhaskar, J. Prestin
We describe an explicit construction of quadrature rules exact for integrating multivariate trigonometric polynomials of a given coordinatewise degree on a spherical triangle. The theory is presented in the more general setting of quadrature formulas on a compact subset of the unit hypersphere, $${\mathbb {S}^q}$$ , embedded in the Euclidean space $${\mathbb {R} ^{q+1}}$$ . The number of points at... hiện toàn bộ
Multi-physics adjoint modeling of Earth structure: combining gravimetric, seismic, and geodynamic inversions
Springer Science and Business Media LLC - Tập 11 - Trang 1-38 - 2020
Georg S. Reuber, Frederik J. Simons
We discuss the resolving power of three geophysical imaging and inversion techniques, and their combination, for the reconstruction of material parameters in the Earth’s subsurface. The governing equations are those of Newton and Poisson for gravitational problems, the acoustic wave equation under Hookean elasticity for seismology, and the geodynamics equations of Stokes for incompressible steady-... hiện toàn bộ
Antiplane deformation of an orthotropic layer due to surface loads
Springer Science and Business Media LLC - Tập 14 - Trang 1-16 - 2023
Anu Chohla, Sunita Rani
In the present paper, analytical expressions for a two-dimensional deformation of a homogeneous, elastically orthotropic layer of finite thickness overlying a rough-rigid base and smooth-rigid base (SRB) caused by surface loads have been obtained. For a two-dimensional approximation, the governing equations are decoupled into two cases: plane strain and antiplane strain case. We have considered an... hiện toàn bộ
On a variational principle for the fractal Wu–Zhang system arising in shallow water
Springer Science and Business Media LLC - Tập 12 - Trang 1-9 - 2021
Yan-Hong Liang, Kang-Jia Wang
The flow of the shallow water of the harbor can be described by the classic Wu–Zhang system. However when the the boundary (such as the coastline) is non-smooth, it becomes invalid. So we modify the classic Wu–Zhang system into its fractal form that can work under the non-smooth boundary by using He’s fractal derivatives. With the help of the semi-inverse method, we establish its fractal variation... hiện toàn bộ
A study of moisture content in unsaturated porous medium by using homotopy perturbation method (HPM) and variational iteration method (VIM)
Springer Science and Business Media LLC - Tập 13 - Trang 1-10 - 2022
Gohar Rehman, Shengwu Qin, Qura Tul Ain, Zaheen Ullah, Muhammad Zaheer, Muhammad Afnan Talib, Qaiser Mehmood, Muhammad Yousuf Jat Baloch, Naveed ur Rahman
Vertical infiltration of water plays an important role in the recharged of contaminated water and enhanced moisture content in the unsaturated porous media. The mathematical model used for such type of phenomenon is Burger's equation. Unsaturated porous media are analyzed by solving Burger's equation using the variational iterative modeling and homotopy perturbation method. When considering all mo... hiện toàn bộ
A mathematical model for analyzing the ground deformation due to a creeping movement across a strike slip fault
Springer Science and Business Media LLC - Tập 10 - Trang 1-20 - 2019
Subhash Chandra Mondal, Suma Debsarma, Sanjay Sen
A long, surface breaking, strike slip fault inclined to the vertical is taken to be situated in a linearly viscoelastic half space of Maxwell type representing the lithosphere–asthenosphere system. Tectonic forces due to mantle convection and other related phenomena are supposed to be acting on the system. Under the action of these forces stresses accumulate in the region and fault undergoes a cre... hiện toàn bộ
Generalized multiscale finite element method for elasticity equations
Springer Science and Business Media LLC - Tập 5 - Trang 225-254 - 2014
Eric T. Chung, Yalchin Efendiev, Shubin Fu
In this paper, we discuss the application of generalized multiscale finite element method (GMsFEM) to elasticity equation in heterogeneous media. We consider steady state elasticity equations though some of our applications are motivated by elastic wave propagation in subsurface where the subsurface properties can be highly heterogeneous and have high contrast. We present the construction of main ... hiện toàn bộ
On the existence of Parker’s ideal bodies
Springer Science and Business Media LLC - Tập 13 Số 1 - 2022
Fernando Sansò
Coupling of multiscale and multi-continuum approaches
Springer Science and Business Media LLC - Tập 8 - Trang 9-41 - 2017
Eric T. Chung, Yalchin Efendiev, Tat Leung, Maria Vasilyeva
Simulating complex processes in fractured media requires some type of model reduction. Well-known approaches include multi-continuum techniques, which have been commonly used in approximating subgrid effects for flow and transport in fractured media. Our goal in this paper is to (1) show a relation between multi-continuum approaches and Generalized Multiscale Finite Element Method (GMsFEM) and (2)... hiện toàn bộ
A study on the reflection of quasi Rayleigh waves in a magneto self reinforced thermoelastic medium with fractional order derivative
Springer Science and Business Media LLC - Tập 14 - Trang 1-24 - 2023
Smita, Rishi Dwivedi, Prashant Kumar Jha
This research looks into a comprehensive investigation of the propagation of quasi Rayleigh waves on the free surface of a self-reinforced thermoelastic medium, considering the presence of fractional order derivatives. The study employs a diverse range of mathematical techniques, including Laplace transformation, harmonic solution, substitution method, and fractional derivative method, to obtain t... hiện toàn bộ
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