karelmatous's blog
A Multiresolution Adaptive Wavelet Method for Nonlinear Partial Differential Equations
A Multiresolution Adaptive Wavelet Method for Nonlinear Partial Differential Equations
If you are interested in the full lecture on the Multiresolution Adaptive Wavelet Method, I have given The Journal of Computational Physics lecture as the part of the Cassyni project.
Computer Graphics Algorithms and Image-Based Multiscale Multigrid Framework
We present a novel image-based multiscale multigrid solver that can efficiently address the computational complexity associated with highly heterogeneous systems. This solver is developed based on an image-based, multiresolution model that enables reliable data flow between corresponding computational grids and provides large data compression. A set of inter-grid operators is constructed based on the microstructural data which remedies the issue of missing coarse grid information.
A nonlinear data-driven reduced order model for computational homogenization with physics/pattern-guided sampling
Developing an accurate nonlinear reduced order model from simulation data has been an outstanding research topic for many years. For many physical systems, data collection is very expensive and the optimal data distribution is not known in advance. Thus, maximizing the information gain remains a grand challenge. In a recent paper, Bhattacharjee and Matous (2016) proposed a manifold-based nonlinear reduced order model for multiscale problems in mechanics of materials. Expanding this work here, we develop a novel sampling strategy based on the physics/pattern-guided data distribution.
Solving Nonlinear PDEs with a priori accuracy using wavelets
We present a numerical method which exploits the biorthogonal interpolating wavelet family, and second-generation wavelets, to solve initial–boundary value problems on finite domains. Our predictor-corrector algorithm constructs a dynamically adaptive computational grid with significant data compression, and provides explicit error control. Error estimates are provided for the wavelet representation of functions, their derivatives, and the nonlinear product of functions.
Google Maps/Earth Computer Graphics Algorithms for Model Reduction in Mechanics of Materials
We present an innovative image-based modeling technique, based on Google Earth like algorithms, to effectively resolve intricate material morphology and address the computational complexity associated with heterogeneous materials. This sharp volumetric billboard algorithm stems from a volumetric billboard method, a multi-resolution modeling strategy in computer graphics. In this work, we enhance volumetric billboards through a sharpening filter to reconstruct the statistical information of heterogeneous systems.
A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials
Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today’s electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials.
A nonlinear manifold-based reduced order model
A new perspective on model reduction for nonlinear multi-scale analysis of heterogeneous materials. In this work, we seek meaningful low-dimensional structures hidden in high-dimensional multi-scale data.
Extreme Multiscale Modeling - 53.8 Billion finite elements
In our recent Extreme Mechanics Letter, we present a simulation consisting of 53.8 Billion finite elements with 28.1 Billion nonlinear equations that is solved on 393,216 computing cores (786,432 threads). The excellent parallel performance of the computational homogenization solver is demonstrated by a strong scaling test from 4,096 to 262,144 cores.