Asymptotic-induced numerical methods for conservation laws

Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques

A fully coupled computational fluid dynamics – agent-based model of atherosclerotic plaque development: Multiscale modeling framework and parameter sensitivity analysis

Background: Peripheral Artery Disease (PAD) is an atherosclerotic disorder that leads to impaired lumen patency through intimal hyperplasia and the build-up of plaques, mainly localized in areas of disturbed flow. Computational models can provide valuable insights in the pathogenesis of atherosclerosis and act as a predictive tool to optimize current interventional techniques. Our hypothesis is that a reliable predictive model must include the atherosclerosis development history. Accordingly, we developed a multiscale modeling framework of atherosclerosis that replicates the hemodynamic-driven arterial wall remodeling and plaque formation. Methods: The framework was based on the coupling of Computational Fluid Dynamics (CFD) simulations with an Agent-Based Model (ABM). The CFD simulation computed the hemodynamics in a 3D artery model, while 2D ABMs simulated cell, Extracellular Matrix (ECM) and lipid dynamics in multiple vessel cross-sections. A sensitivity analysis was also performed to evaluate the oscillation of the ABM output to variations in the inputs and to identify the most influencing ABM parameters. Results: Our multiscale model qualitatively replicated both the physiologic and pathologic arterial configuration, capturing histological-like features. The ABM outputs were mostly driven by cell and ECM dynamics, largely affecting the lumen area. A subset of parameters was found to affect the final lipid core size, without influencing cell/ECM or lumen area trends. Conclusion: The fully coupled CFD-ABM framework described atherosclerotic morphological and compositional changes triggered by a disturbed hemodynamics

Measuring mental workload with EEG+fNIRS

We studied the capability of a Hybrid functional neuroimaging technique to quantify human mental workload (MWL). We have used electroencephalography (EEG) and functional near-infrared spectroscopy (fNIRS) as imaging modalities with 17 healthy subjects performing the letter n-back task, a standard experimental paradigm related to working memory (WM). The level of MWL was parametrically changed by variation of n from 0 to 3. Nineteen EEG channels were covering the whole-head and 19 fNIRS channels were located on the forehead to cover the most dominant brain region involved in WM. Grand block averaging of recorded signals revealed specific behaviors of oxygenated-hemoglobin level during changes in the level of MWL. A machine learning approach has been utilized for detection of the level of MWL. We extracted different features from EEG, fNIRS, and EEG+fNIRS signals as the biomarkers of MWL and fed them to a linear support vector machine (SVM) as train and test sets. These features were selected based on their sensitivity to the changes in the level of MWL according to the literature. We introduced a new category of features within fNIRS and EEG+fNIRS systems. In addition, the performance level of each feature category was systematically assessed. We also assessed the effect of number of features and window size in classification performance. SVM classifier used in order to discriminate between different combinations of cognitive states from binary- and multi-class states. In addition to the cross-validated performance level of the classifier other metrics such as sensitivity, specificity, and predictive values were calculated for a comprehensive assessment of the classification system. The Hybrid (EEG+fNIRS) system had an accuracy that was significantly higher than that of either EEG or fNIRS. Our results suggest that EEG+fNIRS features combined with a classifier are capable of robustly discriminating among various levels of MWL. Results suggest that EEG+fNIRS should be preferred to only EEG or fNIRS, in developing passive BCIs and other applications which need to monitor users' MWL

Hands off Coding

The goal of this paper is to present a versatile framework for solution verification of PDEs. We first generalize the Richardson Extrapolation technique to an optimized extrapolation solution procedure that constructs the best consistent solution from a set of two or three coarse grid solution in the discrete norm of choice. This technique generalizes the Least Square Extrapolation method introduced by one of the author and W.Shyy. We second establish the conditioning number of the problem in a reduced space that approximates the main feature of the numerical solution thanks to a sensitivity analysis. Overall our method produces an a posteriori error estimation in this reduced space of approximation. The key feature of our method is that our construction does not require an internal knowledge of the software neither the source code that produces the solution to be verified. It can be applied in principle as a postprocessing procedure to off the shelf commercial code. We demonstrate the robustness of our method with two steady problems that are respectively an incompressible back step flow test case and a heat transfer problem for a battery. Both test cases are solved by the Finite Element package ADINA. Our error estimate might be ultimately verified with a near by manufactured solution. While our procedure is systematic and requires numerous computation of residuals, one can take advantage of grid computing to get quickly the error estimate

Updates on the Virtual Prairie Project.

communication oral

Non Overlapping Domain Decomposition for Singularly Perturbed Elliptic Boundary Value Problems

: We analyze the Funaro-Quarteroni alternative procedure for the solution of singular perturbation problems. We show that for an appropriate choice of the domain decomposition, one obtains a fast convergent iterative scheme with no relaxation that resolves the boundary layers. The convergence is superlinear with respect to the singular perturbation parameter ffl in the following sense: the amplification factor is o(ffl). We give sharp estimates of the interface position and convergent rates for an homogeneous domain decomposition in one dimensional space as well as in two dimensional space problems on a disk. We extend our results to heterogeneous domain decomposition arising in a simplified model of an electromagnetic problem. We report on implementation results with finite difference approximations and finite element codes (Modulef). Key-words: singular perturbations, boundary layers, transition layers, asymptotic analysis, domain decomposition, iterative methods (R'esum'e : tsvp) ..