Randomized Local Model Order Reduction

In this paper we propose local approximation spaces for localized model order reduction procedures such as domain decomposition and multiscale methods. Those spaces are constructed from local solutions of the partial differential equation (PDE) with random boundary conditions, yield an approximation that converges provably at a nearly optimal rate, and can be generated at close to optimal computational complexity. In many localized model order reduction approaches like the generalized finite element method, static condensation procedures, and the multiscale finite element method local approximation spaces can be constructed by approximating the range of a suitably defined transfer operator that acts on the space of local solutions of the PDE. Optimal local approximation spaces that yield in general an exponentially convergent approximation are given by the left singular vectors of this transfer operator [I. Babu\v{s}ka and R. Lipton 2011, K. Smetana and A. T. Patera 2016]. However, the direct calculation of these singular vectors is computationally very expensive. In this paper, we propose an adaptive randomized algorithm based on methods from randomized linear algebra [N. Halko et al. 2011], which constructs a local reduced space approximating the range of the transfer operator and thus the optimal local approximation spaces. The adaptive algorithm relies on a probabilistic a posteriori error estimator for which we prove that it is both efficient and reliable with high probability. Several numerical experiments confirm the theoretical findings.Comment: 31 pages, 14 figures, 1 table, 1 algorith

Randomized model order reduction

The singular value decomposition (SVD) has a crucial role in model order reduction. It is often utilized in the offline stage to compute basis functions that project the high-dimensional nonlinear problem into a low-dimensional model which is then evaluated cheaply. It constitutes a building block for many techniques such as the proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). The aim of this work is to provide an efficient computation of low-rank POD and/or DMD modes via randomized matrix decompositions. This is possible due to the randomized singular value decomposition (rSVD) which is a fast and accurate alternative of the SVD. Although this is considered an offline stage, this computation may be extremely expensive; therefore, the use of compressed techniques drastically reduce its cost. Numerical examples show the effectiveness of the method for both POD and DMD

PENGARUH LATIHAN SATRIA NUSANTARA TINGKAT PRADASAR-DASAR TERHADAP PENURUNAN HORMON STRESS (KORTISOL)

This research study is aimed at revealing the influence of stressors in Satria Nusantara pre-elementary breathing exercise training towards the reduction of the level of stress hormone (Kartisol). This is an experimental research, using Randomized pretest-posttest control group design. The number of samples used in the treatment group and control group is 15 people respectively. Elisa method was used as the technique of laboratory examination. Data analysis was done through t-test, using SPSS program for Windows. Based on the results of t test analysis on Kartisol variables, there were significant differences between treatment group and control group with p = 0.002 (p <0.05). In this Kartisol variables, there was also reduction in treatment groups of 4.77 ng/ml and 0.83 ng/ml in the control group. The difference was due to breathing exercise treatment using breath control and dhikr so that psychologically treatment group will be more calm, relaxed compared to the control group. Thus breathing exercise can be one of the cheap, effective alternative exercise to reduce stress hormone levels (Kartisol). With relatively low levels of Kartisol, it will provide an opportunity for lymphocytes T to produce interleukin 2 (Th1) and interleukin 4 (Th2). Interleukin will stimulate plasma cells to produce immunoglobulin. By the increase of the activity of plasma cells, IgG also indirectly increases. Thereby, the reduction of Kartisol has a positive influence on the increase of immunoglobulin G. Based on the findings, the Satria Nusantara breathing exercise can be used as a model of alternative sports in order to improve body endurance. Key words: Influence, breathing exercise, reduction, Kartisol