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P. H. GUNAWAN
Universitas Telkom
Mathematics

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PARALLEL COMPUTING FOR BLURRING IMAGE USING MEAN AND WEIGHTED AVERAGE METHOD M. REZA SYAHZIAR; P. H. GUNAWAN
E-Jurnal Matematika Vol 7 No 1 (2018)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2018.v07.i01.p178

Abstract

Blurring is one of the basic image processing technique in order to reduce the noise in a image. In this paper two methods of blurring which are called mean and weighted average method will be elaborated. Three different sizes of mask (3 × 3, 5 × 5 and 7 × 7) are given for each method. Moreover, three different of resolution images 1000 × 1000, 700 × 700, and 400 × 400 pixels are used. From the experiment result, the output image by mean method is shown a darker than the weighted average method. Additionally, run time of CPU using mean method is around 77.78 % shorter than weighted average method.
SIMULASI PERGERAKAN RUNTUHAN LONGSOR MENGGUNAKAN MODEL SAVAGE-HUTTER DENGAN FINITE VOLUME METHOD ALIFANDA PINKAN LUDICA; P. H. GUNAWAN; ANIQ A. ROHMAWATI
E-Jurnal Matematika Vol 7 No 2 (2018)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2018.v07.i02.p189

Abstract

The avalanche is simulated using the Savage-Hutter model with Finite Volume Method (FVM) as a numerical solution in one dimension. The scheme used in FVM is collocated-grid. The aim of this research is to observe the avalanche based on different sediment types on the incline bed with the same initial sediment height. These simulations produce the value of velocity and height avalanche. For each type of sediment has a difference in velocity and height of avalanche affected by the internal angle of friction and the bed friction angle. Sediments with the highest bed friction angle have highest speed. The average velocity of each sediment are Quartz with u = 10.627, Yellow Sand with u = 7.437, and Rice with u = 2.1178 at time t = 1.
SIMULASI GELOMBANG AIR DANGKAL UNTUK PEMBANGKIT ENERGI OSCILLATING WATER COLUMN EKA ANDHIKA KURNIAWAN; ANNISA ADITSANIA; P. H. GUNAWAN
E-Jurnal Matematika Vol 7 No 1 (2018)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2018.v07.i01.p180

Abstract

Development of human causes the increasing of the demand of energy for living. Sea wave energy is one of the alternative energy sources which is renewable and sustainable, no impact on environmental pollution. The goal of this paper is to simulate the level of water wave using shallow water equation for generating energy oscillating water column. The solution of the equation is approximated using LaxFriedrich scheme and will be compared with the analytic solution in standing wave problem. Simulation is used to obtain the results of the energy in the form of electrical power generated by ocean wave. The results of the error of numerical validation is obtained 0.32%. Moreover, the results of the potential energy depend on the height of the surface waves is found 1574.46 Watts the average of water level is 0.881 meters.
ANALISIS KONVERGENSI METODE BEDA HINGGA DALAM MENGHAMPIRI PERSAMAAN DIFUSI F. MUHAMMAD ZAIN; M. GARDA KHADAFI; P. H. GUNAWAN
E-Jurnal Matematika Vol 7 No 1 (2018)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2018.v07.i01.p176

Abstract

The diffusion equation or known as heat equation is a parabolic and linear type of partial differential equation. One of the numerical method to approximate the solution of diffusion equations is Finite Difference Method (FDM). In this study, the analysis of numerical convergence of FDM to the solution of diffusion equation is discussed. The analytical solution of diffusion equation is given by the separation of variables approach. Here, the result show the convergence of rate the numerical method is approximately approach 2. This result is in a good agreement with the spatial error from Taylor expansion of spatial second derivative.
KONVERGENSI NUMERIK FLUKS RUSANOV DAN HLLE PADA METODE BEDA VOLUM UNTUK MENGHAMPIRI PERSAMAAN AIR DANGKAL EKO MEIDIANTO N. R.; P. H. GUNAWAN; A. ATIQI ROHMAWATI
E-Jurnal Matematika Vol 7 No 2 (2018)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2018.v07.i02.p190

Abstract

This one-dimensional simulation is performed to find the convergence of different fluxes on the water wave using shallow water equation. There are two cases where the topography is flat and not flat. The water level and grid of each simulation are made differently for each case, so that the water waves that occur can be analyzed. Many methods can be used to approximate the shallow water equation, one of the most used is the finite volume method. The finite volume method offers several numerical solutions for approximate shallow water equation, including Rusanov and HLLE. The derivation result of the numerical solution is used to approximate the shallow water equation. Differences in numerical and topographic solutions produce different waves. On flat topography, the rusanov flux has an average error of 0.06403 and HLLE flux with an average error of 0.06163. While the topography is not flat, the rusanov flux has a 1.63250 error and the HLLE flux has an error of 1.56960.
SIMULASI NUMERIK PADA ALIRAN AIR TANAH MENGGUNAKAN COLLOCATION FINITE ELEMENT METHOD UMMU SALAMAH; ANNISA ADITSANIA; P. H. GUNAWAN
E-Jurnal Matematika Vol 7 No 1 (2018)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2018.v07.i01.p177

Abstract

This research presents a numerical simulation on groundwater flow using collocation finite element method (CFEM). Groundwater flow is known as the flow of water beneath the soil. Generally, groundwater flow is generated due to high hydraulic differences. The CFEM is an approximation solution of the differential equation by assuming the selected analytical function to fulfill the differential equation and setting the residual value turn out zero. Here, this research will discuss the case of groundwater flow on steady state and unsteady state. The results of numerical method CFEM is shown second order in terms of convergence by error. The numerical error in case of constant water flow is obtain 3.62E ? 23 using the grid size 6.1797e ? 07. Moreover, the flow of groundwater is simulated in various of hydraulic conductivity constants.
ANALISIS ALIRAN DARAH DALAM PEMBULUH ARTERI MENGGUNAKAN PERSAMAAN NAVIER-STOKES DAN METODE LATTICE-BOLTZMANN FATHURAHMAN MA’RUF HUDOARMA; P. H. GUNAWAN; ANIQ A. ROHMAWATI
E-Jurnal Matematika Vol 7 No 2 (2018)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2018.v07.i02.p191

Abstract

This simulation was performed to analyze arterial blood flow using Navier-Stokes equations and LatticeBoltzmann method with Bhatnagar-Gross-Krook approach to obtain an explicit form of the LatticeBoltzmann Bhatnagar-Gross-Krook equations. Then by adding some cases of plaque on simulation domain, changes in arterial blood flow pressure can be analyzed. The area and shape of the plaque cause narrowing the artery vessels that affect the pressure and rate of blood flow dynamically. The pressure of blood flow without plaque is stable ranged from 17 to 19 Pa. While in the vessels with plaque, blood flow pressure increased significantly up to 35.145 Pa.
Co-Authors A. ATIQI ROHMAWATI ALIFANDA PINKAN LUDICA ANIQ A. ROHMAWATI Annisa Aditsania EKA ANDHIKA KURNIAWAN EKO MEIDIANTO N. R. F. MUHAMMAD ZAIN FATHURAHMAN MA’RUF HUDOARMA M. GARDA KHADAFI M. REZA SYAHZIAR UMMU SALAMAH