Judul: The Design and Implementation of Sparse Matrices in RLaB
Abstrak: RLaB merupalcan bahasa pemrograman yang digunakan untuk membantu menyelesaikan permasalahan matematika dengan menggunakan metode numerik. Secara umum struktur data RLaB menggunalcan struktur data matriks atau larik (array) dua dimensi. Sampai dengan versi 1.19b, RLaB hanya mampu menampung paling banyalc 4.500.032 byte atau sebanyalc 562.504 elemen (setiap elemen membutuhkan 8 byte). Sehingga untuk menyimpan matriks jarang, yang dewasa ini cenderung mulai banyalc digunalcan, perlu dilakukan upaya efisiensi struktur penyimpanan elemen matriks jarang, misalnya dengan hanya menyimpan elemen talc nolnya saja. Berkaitan dengan hal tersebut, malca dalam tulisan ini alcan dipelajari struktur penyimpanan elemen matriks jarang pada RLaB. Selain itu, alcan disusun fungsi library operasi aritmatika matriks dengan menggunalcan struktur matriks jarang, dan membandingkan besarnya ukuran matriks yang dapat disimpan antara struktur matriks jarang dan matriks penuh serta waktu eksekusi pada program iterasi Conjugate Gradients (CG) dan Conjugate Gradients Least-Squares (CGLS)). Struktur penyimpanan matriks jarang dalam RLaB dapat direpresentasikan dengan metode skema koordinat dan metode kumpulan vektor jarang. Metode skema koordinat dapat direpresentasikan dengan struktur data list dan struktur data larik, sedangkan metode kumpulan vektor jarang hanya dapat direpresentasikan dengan struktur larik saja. Metode skema koordinat dengan struktur larik alcan efisien digunalcan jika jumlah elemen talc no! pada matriks jarang kurang dari sepertiga jumlah elemen seluruhnya. Metode skema koordinat yang direpresentasikan dengan struktur list akan efisien digunalcan pada setiap matriks jarang yang elemen tak nolnya kurang dari jumlah elemen seluruhnya, sedangkan metode kumpulan vektor jarang alcan efisien digunalcan jika jumlah elemen talc nolnya kurang dari setengah jumlah elemen seluruhnya dikurangi dengan jumlah baris matriks. Dengan menggunalcan metode skema koordinat yang direpresentasikan dengan struktur data list, dapat dibuat suatu fungsi library operasi aritmatika matriks (penjumlahan dua matriks, perkalian dua matriks, perkalian matriks dengan vektor, hasil kali matriks dengan skalar dan transpose matriks). Dari hasil uji pada program iterasi CG dan CGLS diketahui bahwa struktur matriks jarang mampu menyimpan matriks jarang dengan ukuran lebih besar tetapi waktu eksekusinya lebih lambat. Kelambatan ini disebabkan oleh pencarian alamat elemen talc nolnya dan pemeriksaan keberadaan suatu elemen memerlukan walctu relatif lama.
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Judul: Interpolasi Multinomial Lagrange di Rn dan Implementasinya dalam MATLAB®
Abstrak: Interpolation is a method to construct a function which goes through a given set of data points. Interpolation is usually implemented in two dimensions. Polynomial Lagrange interpolation is one of formulas that used in R². The purposes of this research are to develop the multinomial Lagrange formula in Rn by reconstructing polynomial Lagrange formula and to build an algorithm of multinomial Lagrange in R³ and its implementation. Systems of linear equations are used as illustration in a process of reconstructing polynomial Lagrange formula. The Vandermonde matrix V is the coefficient matrix of the system. The column vectors of the solution of system are coefficients of interpolation function. A method to reconstruct polynomial Lagrange formula is developed by substituting the rows of Vandermonde matrix V with monomial basis. This method is the basic of construction of multinomial Lagrange interpolation in R". The method is applied by adapting the basis used which is a multinomial basis. An algorithm of multinomial Lagrange interpolation in R³ has been constructed and implemented using MATLAB®. The result of the computation shows that the algorithm is able to work properly.
Keyword: Lagrange interpolation, multinomial basis, Vandermonde matrix

Judul: Thermal Characteristics and Dynamics of Tropical Cyclone over Western North Pacific Ocean: A Case Study of Typhoon Songda (Chedeng) 2011
Abstrak: The frequent occasion of Tropical Cyclone (TC) over Western North Pacific (WNP) Ocean lies from 10˚N to 26˚N and 121˚E to 170˚E. Sources of TC development come from warm ocean temperature where latent heat is released during condensation processes and subsequently concentrated in the boundary layer. Relative humidity at 850-700 hPa is responsible to produce the most intense storm. Meanwhile, weak vertical wind shear between 850-200 hPa is one of the dynamical factors that lead to the development of TC. Pressure level of 850-200 hPa is chosen to minimize the thermodynamic effect in the lower troposphere. Typhoon Songda (Chedeng in the Philippines) or TSC lasted from May 18th to 30th, 2011 and strengthened into powerful Super Typhoon stage between May 24th and 27th. Long curving track and the exhibition of all sequences of TC life cycle, TSC is then considered as an ideal case of TC. The objective of the study with case of TSC is to investigate the role of thermal characteristics and dynamics on TC intensity. The research is carried out by using Advanced Research of Weather Research and Forecasting model (WRF ARW model) version 3.3. Two domains are employed in the model. The first domain situate from 02˚N to 40˚N and 118˚E to 149˚E and cover spatial resolution () of 33.1 km. The second domain situate from 09˚N to 27˚N and 119˚E to 132˚E with of 11 km. Timestep of the model () is 120 seconds. The model is supported by the following physical parameterization, i.e., Yonsei University Scheme (YSU) in the boundary layer, Kain-Fritsch scheme (KF) in the cumulus, and WRF Single-Moment 3-class scheme in the microphysics. Initial meteorological condition prior to the formation of the cyclone is generated using WRF ARW standard-release model. Sensitivity of the model output is obtained from a selected single-parameter change scenarios, namely, 10 % to 20 % decrease and increase of wind shear initial data at 850-200 hPa, and by 10 % to 20 % decrease of relative humidity initial data at 850-700 hPa. The result showed that the negative correlations between wind shear and intensity are found in wind shear scenarios. Wind shears of 10 ms-1 which lead to strengthening of the wind intensity in the early period of Typhoon development are found in wind shear scenarios. The effect of wind shear changes on wind intensity is statistically significant in the 20 % wind shear scenarios. During mature stage, weak wind intensity occurred when wind shear increase as given in the WRF standard-release and the 20 % decreasing scenario. Different situation is found in the 20 % increasing scenario where wind shear tend to weak and lead to strong wind intensity at this stage. Meanwhile, the reduction of moisture supply at 850-700 hPa resulting from 20 % decreasing relative humidity play a major role in the weakening of wind intensity and reduces mechanical energy of the cycle process as much as 300 J kg-1.
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