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"Skripsi ini membahas tentang metode pendekatan numerik dari perilaku material polycristal elasto-viscoplastik melalui penetapan Volume _l_mentaire repr_sentatif (VER) atau dimensi minimum yang mampu merepresentasikan perilaku material secara umum yang diselesaikan dengan metode homogenisasi untuk mendapatkan comportement effectif berbasis pada metode penyelesaian Runge-Kutta orde 4 dan transformasi Fourier. Tujuan akhir skripsi ini adalah menghasilkan model matematis yang akurat untuk menggambarkan perilaku material polycristal elasto-viscoplastik.

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The focus of this study is to produce an numerical estimation of the effective behavior of of elasto-viscoplastic polycrystal materials through the means of Volume _l_mentaire repr_sentatif (VER) or the minimum dimension needed to represent the characteristics of the material which is solved with the homogenization method to obtain the comportement effectif based on the Runge-Kutta 4th order method and Fourier Transforms. The desired output of this study is to produce an accurate mathematical model to describe the effective behavior of elasto-viscoplastic polycrystal materials."

"A concise survey of the current state of knowledge in 1972 about solving elliptic boundary-value eigenvalue problems with the help of a computer. This volume provides a case study in scientific computing -- the art of utilizing physical intuition, mathematical theorems and algorithms, and modern computer technology to construct and explore realistic models of problems arising in the natural sciences and engineering."

"During the last decade, water scarcity in terms of quantity and quality degradation has become a major issue in Indonesia. In 2006, Universitas Indonesia (UI) supported by the Ministry of Public Works built a recharge pond as a field model to overcome flood and drought in Jakarta and its surroundings. However, since then, a lack of research has been conducted to monitor and analyze the rate of change in water quality in the UI recharge pond. The purposes of this study are to identify the characteristics of UI recharge pond and evaluate the surface water quality changes. Water samples were taken from the pond and analyzed in the laboratory for water quality tests. The evaluation method used for simulation of water quality was a numerical model using Runge-Katta Order 4. Laboratory analysis results show concentrations of Mn, Fe, BOD and COD are exceeding the water quality standards (GR No.82/2001). The water purification process in the pond was found to be faster in response to BOD (?= 0.5 d-1) and for Mn, Fe, and COD are found to have similar results at ?= 0.4 d-1. The 95% response time of the pond was found to be longer for Mn, Fe, and COD (t95 = 7.5 d) and the faster rate is BOD (t95 = 6.0 d). The result of numerical modeling demonstrates Mn concentration in the pond will be doubled (0.45 mg/L) on the day-15th and asymptotically converges on a steady state. The Fe, BOD, and COD reaches the steady state concentration around on the day-11th (0.95 mg/L), on the day-13th (56.6 mg/L), and on the day-17th (224 mg/L), respectively."