In our proposed iteratively adaptive method, we achieve this global-to-local information transfer through the combination of coarse-mesh solving using adaptive multi-scale basis functions and fine-mesh smoothing operations.
In each iteration step, we first update the multi-scale basis functions based on the approximate numerical solutions of the previous iteration steps, and obtain the coarse-mesh approximate solution using a Galerkin projection.
Convergence analysis of the proposed algorithm is carried out under the framework of two-level multi-grid method, and the harmonic coordinates are employed to establish the approximation property of the adaptive multi-scale basis functions.
The choice of the local boundary conditions for the multi-sale basis functions determines the accuracy of the MsFEM numerical solution, and one needs to incorporate the global information of the elliptic equation into the local boundary conditions of the multi-scale basis functions to recover the underlying fine-mesh solution of the equation.
Fees are on a sliding scale basis.
On one side, the series focuses on recent methods and technologies which allow multi-scale, multi-physics, high-resolution analysis and modeling of biological systems.
A multi-scale supervised neural architecture, called Multi-Scale SOON, is proposed for natural texture classification.
Zhao, X. Multi-scale multi-mechanism design of tough hydrogels: Building dissipation into stretchy networks.
Hahn, O. & Abel, T. Multi-scale initial conditions for cosmological simulations.
Characterization and Measurement of Multi-Scale Gas Transport in Shale Core Samples.
Alessandretti, L., Sapiezynski, P., Lehmann, S. & Baronchelli, A. Multi-scale spatio-temporal analysis of human mobility.
