Reduced Basis Numerical Homogenization for Scalar Elliptic Equations with Random Coefficients: Application to Blood Micro-circulation
نویسندگان
چکیده
We consider a non periodic homogenization model designed to simulate the blood flow at the level of the micro-vascularised tissues. We solve elliptic partial differential equations with two length-scales on the domain and we use the reduced-basis method to speed up the numerical resolution. Finally, we show numerical results and comparisons in 2D and 3D.
منابع مشابه
Homogenization of random elliptic systems with an application to Maxwell ’ s equations ∗
We study the homogenization of elliptic systems of equations in divergence form where the coefficients are compositions of periodic functions with a random diffeomorphism with stationary gradient. This is done in the spirit of scalar stochastic homogenization by Blanc, Le Bris and P.-L. Lions. An application of the abstract result is given for Maxwell’s equations in random dissipative bianisotr...
متن کاملNumerical Homogenization and Correctors
In this paper we consider numerical homogenization and correctors for nonlinear elliptic equations. The numerical correctors are constructed for operators with homogeneous random coefficients. The construction employs two scales, one a physical scale and the other a numerical scale. A numerical homogenization technique is proposed and analyzed. This procedure is developed within finite element ...
متن کاملNumerical homogenization and model order reduction for multiscale inverse problems
A new numerical method based on numerical homogenization and model order reduction is introduced for the solution of multiscale inverse problems. We consider a class of elliptic problems with highly oscillatory tensors that varies on a microscopic scale. We assume that the micro structure is known and seek to recover a macroscopic scalar parametrization of the microscale tensor (e.g. volume fra...
متن کاملNumerical homogenization of a nonlinearly coupled elliptic-parabolic system, reduced basis method, and application to nuclear waste storage
We consider the homogenization of a coupled system of PDEs describing flows in heterogeneous porous media. Due to the coupling, the effective coefficients always depend on the slow variable, even in the simple case when the porosity is periodic. Therefore the most important part of the computational time for the numerical simulation of such flows is dedicated to the determination of these coeff...
متن کاملMultiscale Numerical Methods for Singularly Perturbed Convection-diffusion Equations
We present an efficient and robust approach in the finite element framework for numerical solutions that exhibit multiscale behavior, with applications to singularly perturbed convection-diffusion problems. The first type of equation we study is the convectiondominated convection-diffusion equation, with periodic or random coefficients; the second type of equation is an elliptic equation with s...
متن کامل