Performance Analysis of One Dimension FDTD Code

Performance Analysis of One Dimension FDTD Code Performance analysis of One dimension FDTD code using Parallel Processing Technique P. GUNAPANDIAN, M.R.SUBASREE, B. MANIMEGALAI Abstract The requirement of longer processing time and larger memory makes FDTD method impractical for many cases. Implementation of parallel processing in FDTD method is proposed in this paper. The implementation depends mainly on computer architecture and programming libraries under different operating systems. In this paper a several performance tests of a one dimension FDTD code is tested in different platforms. The results shows that Parallel processing shows a linear decrease in time and larger data handling which makes it as a right platform for complex structures. Keywords:  FDTD, parallel processing, computer architecture, operating system, serial processing. Introduction Computational ability has advanced in the recent few decades. One of the most common methods to solve Maxwells equations on arbitrary configurations of materials and field sources is the Finite Differences on Time Domain (FDTD) [1]. There exist a number of techniques for enhancing the performance of the conventional FDTD, in order to obtain accuracy the conformal FDTD method which simulates the curved perfect electrical conductor (PEC) [2,3]. Sub-gridding technique is used to increase the mesh density in the local area in which the field varies quickly [5,6]. The Multi-Resolution Time-Domain (MRTD) and Pseudo-Spectrum Time-Domain (PSTD) techniques are used to reduce the dispersion of the conventional yee grid [7,8]. The above techniques mentioned are used to improve the conventional FDTD technique for the purpose of reducing either memory requirements or simulation time. The parallel-processing FDTD accelerates the FDTD simulation by distributing the job to multiple processors, so th at the available memory for large problems is virtually unlimited. At the same time, the simulation time is dramatically reduced compared to a single-processor implementation. On the computational point of view the parallel processing have an important advantage which makes the parallel executions strategies easier. Parallel processing in computers is based on dividing a computer code into a number of segments and distribution of the task among a number of computers/processors, which are then executed in parallel. This may be achieved on hardware-level, software level, or both. Hardware-level parallelization necessitates alternative processor designs. Software-level parallelization can be either on data level or function level, depending on the characteristics of the code [9]. In this paper one dimensional FDTD code is developed for parallel processing. The performance analysis of the code developed is compared with both serial and parallel. The code is simulated in different platforms and the results are obtained. The results shows the efficiency of the parallel processing in handling larger data and reduction of time compared to serial processing. FDTD METHOD The FDTD method is one of the well known approaches to solve Maxwell’s partial differential equations, because of its high versatility. FDTD algorithm is based on temporal and three-dimensional spatial discretization and it transforms the time-dependent Maxwell’s curl equations into a set of finite-difference relations [10, 11].Boundary conditions are needed on the edge of the simulation domain, among the several possible choices perfect matched layer (PML) boundary can be more accurate and the PML boundary is used in the developed code. One Dimension FDTD The one dimension FDTD starts with the formulation of the Maxwell’s equations, Where E and H are electric and magnetic field respectively. The one dimension equation for Ex and Hy are given, which denotes the Electric field with respect to x direction and magnetic field with respect to y direction. The update equations are given in (3) and (4). The FDTD update equations are used to develop the Matlab code and the code is excited with the Gaussian pulse and the results are obtained. PARALLEL FDTD According to the principle of FDTD algorithm, the electromagnetic field value at certain position can be decided by the value of last time step at this position and electromagnetic field value of this time step at nearby position. The electromagnetic field value has no direct relation to the values at position far from this point. So, the whole computational space can be divided into some sections that can be computed in some nodes of parallel computing system. The exchange of field values between nodes can be executed only at interface between sections. According to the basic concept, the computing between parallel nodes can be executed to simulate the serial computing in a single PC or workstation. This is the key point of our parallel FDTD algorithm. Fig.1 shows the methodology of serial and the parallel approach Figure 1. Serial and parallel approach PARALLEL PROCESSING TECHNIQUE The main idea of parallel processing starts with the updating the EM field components in each processor in the same instant. When the computation updates a field component on the border of the domain, some values belonging to the border of the adjacent domain are required to avoid communications during the computations each sub domain is surrounded by the border cells of the other domain. These border values are communicated after the updating phase. Thus the parallel processing is achieved. The first step of the FDTD modeling starts with the one dimensional method. A Gaussian pulse is generated in the centre of the problem space and the pulse propagates in the both the directions. The time step is taken to be 500 iteration steps and the total time required for the signal is 500fs. The time seconds are calculated by the time taken by the pulse to originate from the centre and to decay at the end. The Matlab code is developed for one dimensional FDTD for serial processing and the code is updated to parallel processing. The number of cells of the computation domain in varied by keeping the number of iterations constant and the time taken by the serial and the parallel processing is noted. The figure2 shows the comparison between the serial and parallel processing for different number of cells. From the figure 2 it is noted that the parallel processing code is able to process the large number of cells within the shorter period of time, thereby proving that the parallel processing can be used to process larger amount of data in shorter duration of time. Figure 2. Serial vs. parallel processing The parallel processing code developed has been simulated in various newer version Intel processors which is used to analyze the performance. The number of iterations are kept constant and the cell size is varied and the code is simulated in different Intel processors include i3, i5, i7 and Pentium processors. The results shows that the updated newer version i7 was able to process the data more quickly, so that the parallel processing can be used more efficiently in higher versions system which is easily available now a days. Figure 3 shows the Comparision with different versions of the processors. From the results it is observed that the i7 processor was able to process the code more efficiently than the others. Pentium processor which is one of the oldest among took larger time to process the code. Figure 3. Parallel processing on different versions of Intel processors The parallel code is simulated with different number of Matlab workers. Figure 4 shows the relation between the parallel code and the number of Matlab workers. In this code the number of iterations is kept constant and the time taken by the code to run with different number of cells is noted. The graph shows that parallel code works more efficiently when the number of workers is increased to be four. Figure 4. Performance with different number of Matlab workers The speed-ups increase with the problem size because of the better exploitation of CPU resources and parallel processing. Figure 5 shows the achieved speed-ups for with respect to the serial algorithm running on the CPU. Thus the parallel processing gives a better speed up for larger problems. Figure 5. Speed up comparison for serial and parallel processing From the figure 5 it is noted that the parallel processing gives a better speed up. With the previous results the number of iterations and the cell size is varied and the results are noted. For each cell size the iterations are changed and the values are noted. Figure 6 shows the speed up for different cell size at various iterations. From the figure it can be absorbed that larger the computation domain better the speed up thereby making the parallel processing very much suitable for larger computation domain. Figure 6. Iteration vs. Speedup CONCLUSION From the results it is observed that the disadvantage of the FDTD method can be overcome by using Parallel processing FDTD method. The performance analysis of this paper thereby shows that the parallel processing can be easily achieved efficiently by using modern CPU’s present today which can be used to do complex computations. REFERENCES [1]. Yee, K. S., Numerical solution of initial boundary value problems involving Maxwells equations in isotropic media, IEEE Transactions on Antennas and Propagation, Vol. 14, No. 5, 302-307, May 1966. [2]. Time Domain Maxwell s Equations Solver: Software and User s Guide, Norwood, MA, Artech House, 2004. [3]. W. Yu and R. Mittra, A Conformal FDTD Software Package for Modeling of Antennas and Microstrip Circuit Components, IEEE Antennas and Propagation Magazine, 42, 5, October 2000, pp. 28-39. [4]. W. Yu and R. Mittra, A Conformal Finite Difference Time Domain Technique for Modeling Curved Dielectric Surfaces,  IEEE Microwave and Guided Wave Letters, January 2001, pp. 25-27. [5]. W. Yu and R. Mittra, A New Sub gridding Method for Finite Difference Time Domain (FDTD) Algorithm, Microwave Opt. Techno. Lett. , 21, 5, June 1999, pp. 3 3 0-333. [6]. B. Wang, Y. Wang, W. Yu, and R. Mittra, A Hybrid 2-D FDTD Sub gridding Scheme for Modeling On-Chip Interconnects, IEEE Transactions on Advanced Packaging, 24, 4, November 200 1 , pp. 528-533. [7]. X. Zhu, T. Dogaru, and L. Carin, Three-Dimensional Biorthogonal Multiresolution Time-Domain Method and Its Application to Electromagnetic Scattering Problems, IEEE Transactions on Antennas and Propagation, AP-51, 5, May 2003, pp. 1085- 1 092. [8]. Q. H. Liu, The PSTD Algorithm: A Time-Domain Method Requiring Only Two Cells Per Wavelength, Microwave Opt. Technol. Lett.,IS,1997, pp. 1 58- 1 65. [9] W. H. Yu, Y. J. Liu, T. Su, N.-T. Huang, and R. Mittra, †A robust parallel conformal finite-difference time-domain processing package using the MPI library,† IEEE Antennas Propagat. Mag., vol. 47, no. 3, pp. 39-59, 2005. [10] Almasi, G.S, and Gohlied, A, â€Å"Highly Parallel Computing†. Benjamin Cummings Publishing, 2a ed., 1994. [11]. Taflove A, Brodwin ME. Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations. IEEE Trans Microwave Theory Tech. 1975,MTT-23(8):623–30. [12]. W. Yu, X. Yang, Y. Liu, and R. Mittra â€Å"Parallel FDTD Performance Analysis on Different Hardware Platforms â€Å",IEEE Int. Symp. Antennas and Propagation Meeting

American Legal and Constitutional History

As residents or citizens of the United States of America, we enjoy certain rights that many people across the world do not have. One of those rights is freedom of speech, which is guaranteed to all of us through the United States Constitution. However, in some instances, our freedom of speech rights can be limited. One of those circumstances involves freedom of political expression. At this point, one would have to ask; how can a democratic country, which, like all other democratic countries, is based on freedom of speech, limit the same under certain conditions?In order to understand why and how this can happen, we will first examine the concept of citizenship and the Constitution of the United States as it relates to freedom of political speech. In addition to that, we will analyze how freedom of speech as it relates to politics can affect security and what affects current legislation has on freedom of speech. Based on the above-mentioned research, I intend to prove that compromisi ng freedom of political expression is a violation of the United States Constitution and as such cannot be allowed.Furthermore, I will argue that passing legislature such as the US Patriot Act can be very dangerous as it provides government with the power to violate our freedom of speech rights. Citizenship In the first part of the paper, we will examine and summarize the concept of citizenship. This is a very extensive process that is defined as â€Å"the process by which some people are included and others are excluded as members of the community† (Walker, 2002). In our country, everybody living here, regardless if citizen or not, enjoys the same protections from the law.The concept of citizenship is important because it associates us with our nation and with the law of the land. â€Å"Essentially, rights granted to citizens are typically represented by a continuum; however, the mere existence of citizenship does not necessarily equate to equivalent representation across th e board, often with glaring inconsistencies across similar geographic locations or historic periods, of which history is rife with examples. † (Gans 2005). So why is citizenship so important? Citizenship is important because it gives everybody the constitutional rights.Nobody can take them away from a United States citizen, regardless of his political views or statements. As United States citizens, we are entitled to a set of rights, which is unique in the world. The United States Constitution entitles us to those rights and guarantees that we can enjoy them. The United States Constitution is the set of documents that embody the principles on which the United States is governed. The Constitution is the supreme law of the land and no other law, at any level of government, can be established without considering the rules and rights as set forth in that document.The part that is especially important to American as it relates directly to their rights is the part of the Constitutio n that is known as the Bill of Rights. The first ten amendments of the United States constitution are more commonly referred to as the â€Å"Bill of Rights,† because they define specific rights that are granted to all United States citizens by the Constitution of the United States. â€Å"The Bill of Rights is modeled on many other similar documents, all of which owe their inception to the Magna Carta, the bill of rights written in England in 1215 CE.The Bill of Rights is considered to be an important part of the Constitution, and is also an integral part of popular culture; most Americans, for example, know what someone means when he or she â€Å"pleads the fifth,† a reference to the Fifth Amendment, which protects people from self recrimination. † (Smith 2003) The part of the Bill of Rights that is of concern to this paper is its First Amendment. According to the First Amendment there are actually several rights guaranteed to all citizens equally. Many people r emember two of them, the right to free speech, and the right to a free press.There are very few exceptions to free speech and fee press. Writing or speaking words that could be constituted as a threat to the American people or seriously threatening the life of someone can definitely lead to a civil law suit or even criminal prosecution. The right to free speech and free press fully includes any political expressions, regardless of what nature. So, if these rights are guaranteed to us, why do some people have concerns about political expression? Political Expression and limitations In wake of the 9/11 attack on United States a very controversial piece of legislation called â€Å"The USA Patriot Act† has been passed.The problem with this legislation lies in its definition of terrorism or terrorist activities. â€Å"The USA PATRIOT Act section 802 defines domestic terrorism so broadly that it could apply to an individual exercising his or her freedom of speech, expression, and assembly through acts of civil disobedience. The Department of Justice has not revealed how it is using section 802†¦ Moreover, Section 215 of the USA PATRIOT Act permits the FBI to seek records from bookstores and libraries of books that a person has purchased or read, or of his or her activities on a library's computer.This change puts people at risk for exercising their free speech rights to read, recommend, or discuss a book, to write an email, or to participate in a chat room, and thus could have the effect of chilling constitutionally protected speech. It also denies booksellers and library personnel the free speech right to inform anyone, including an attorney that the FBI has asked for someone's reading list. † (BORDC, 2008) Since then the BORDC has documented several cases where individual rights to free speech have been violated as a direct result of this legislature.Many of these violations have been triggered by political activity. For example â€Å"In June 2 004, Buffalo, New York, artist Steve Kurtz was detained by law enforcement and had his home searched by FBI agents. Despite finding only harmless substances, which Kurtz uses in his politically motivated art projects, the FBI proceeded with a Grand Jury hearing to decide whether to indict Kurtz under the USA PATRIOT Act’s biological agents provision. On June 29th, Kurtz’s bio-terrorism related charges (USA PATRIOT Act section 817) were dropped. † (BORDC, 2003)The above mentioned instance, along with similar mistakes have led many people to believe that our rights to free speech, including and especially the right to political expression, have been limited by legislature such as and similar to the Patriot Act. Many however argue that such laws are necessary in order to protect the greater good and help decrease the chances for renewed attacks on the United States. Another example of limitation of political expression involves a very recent incident at the Universi ty of Berkeley in California.The City Council sent a letter to the United States Marines recruiting office stating that their recruiters were not welcome in the city or on campus. This was just a letter of statement and it contained no threats or any other suggestions of violence, protests, or demonstrations. In return for this action, which was seen as very anti-patriotic by many politicians and citizens, various pressures were placed upon the city. â€Å"Some lawmakers were threatening to withhold millions of dollars of federal and state funding to the school as retaliation.They claimed that since U. S. Marines are not good enough for Berkeley, then neither were taxpayers’ dollars†¦ After receiving significant heat, the officials decided to recognize the officials’ right to be in Berkeley and clarified their position saying they support US troops — just not the war and the recruitment of young people. (Hill, 2008) The problem that we face here is that a political view of a cities population, as reflected in the council letter, was oppressed through threats of funding elimination.Even though the political view reflected in the letter is not popular and inappropriate, that was barely an exercise of free political speech that was suppressed by threats. The fact that this happened on a college campus, which should facilitate learning through open debate, makes it especially bad as it sends a statement that everybody should be politically in line with the main stream. â€Å"†¦in dealing with college campuses (as the cultivating grounds for those of the future) we should be more understanding when sentiments show up and give them room to thrive if they wish.Suppression, such as financial deprivation, is no way to deal with a situation and absolutely no way to stifle a conflict. † (Hill, 2008). This opens the question about why political expression matters and what is so special about it? Political Expression and Democracy In order to understand the impact of free speech on a democratic society we have to analyze the basics of democracy. â€Å"Freedom of speech and expression, especially about political and other public issues, is the lifeblood of any democracy.Democratic governments do not control the content of most written and verbal speech. Thus democracies are usually filled with many voices expressing different or even contrary ideas and opinions. † (U. S. Department of State, 2008) This statement is a very effective summary in reference to importance of free speech. As a democratic government, our leadership is supposed to lead is in direction that we chose. This choosing of direction is most often done through political debates as we see them on TV.â€Å"Democracy depends upon a literate, knowledgeable citizenry whose access to information enables it to participate as fully as possible in the public life of their society and to criticize unwise or tyrannical government officials or polici es. Citizens and their elected representatives recognize that democracy depends upon the widest possible access to uncensored ideas, data, and opinions†¦ For a free people to govern themselves, they must be free to express themselves — openly, publicly, and repeatedly; in speech and in writing. † (U. S. Department of State, 2008)What we have to understand is the fact that free flow of ideas through speech and other forms of communication is essential for the survival of a democratic government and as such, it cannot be compromised in any way. Free speech creates a pool of ideas that allow us to come to the bottom of every issue at hand by finding the truth. At the same time, we cannot afford to misunderstand this concept. Many people in history have favored freedom of speech, but only the kind of speech that they agreed with. This is why we had to deal with people like Hitler, Stalin, and Saddam.Their view of freedom of speech, especially when it came to politics, was definitely a one-way street. By using them as an example, we need to make sure that we focus on allowing all views to be expressed, regardless whether we agree with them. In my opinion, in this country, we cannot afford to place any limitations on freedom of political speech. Another issue that is directly related to the freedom of speech is freedom of belief. If the government or any other institution attempts to limit our freedom of political expression, then at the same time, they are prohibiting us from having the freedom to believe what we want.The concept is very simple. If we cannot freely express our ideas, then we should not have them in a first place. Many countries across the world had such a system in place. Saddam’s Iraq, Stalin’s Soviet Union and others. The reason these governments were called totalitarian was the fact that their citizens could not freely express their ideas and political views. This proves the fact that freedom of political expressi on is what makes us a strong democracy and that it should not be compromised. Many supporters of limited free speech cite various examples where it was necessary to limit political expression in order to achieve a greater good.One such example is Germany and many argue that by prohibiting political parties and any association with them (Nazi Party) was the right thing after World War II. I fully agree with that. However, when we cannot compare Germany and the United States (at least not back at that time). German people back then did not know the concept of democracy. Ones it was introduced they accepted it and Nazis never resurfaced again. In any case, my point is that in order to help nations such as post world war II Germany reach the right conclusion and adopt democracy some drastic measures may be necessary.However, these measures should never be undertaken on our soil. We have a healthy democracy and any limitations would disturb the balance. Even though it should never be com promised, freedom of speech has some limitations. One of the limitations that is relevant to political expression is the use of fighting words. The fact is that he inflammatory nature of some speeches can cause the listener to direct violence at the speaker or other target groups as defined by the speaker. Additionally, â€Å"fighting words† have become limited to speech directed to one person and not to speech directed generally at a crowd.The idea is that if a speech is going to cause harm to somebody or limit him or her in enjoyment of his or her constitutional rights in any way, then it is prohibited. Another major issue that has come out of this is the fact that many state universities prohibit speeches that are offensive to minorities. Universities have adopted those policies in order to respond to complaints of those who are subjects of hateful speeches. â€Å"That's the wrong response, well-meaning or not. The First Amendment to the United States Constitution protect s speech no matter how offensive its content.Speech codes adopted by government-financed state colleges and universities amount to government censorship, in violation of the Constitution. And the ACLU believes that all campuses should adhere to First Amendment principles because academic freedom is bedrock of education in a free society. † (ACLU, 2008) This is a very important issue that demonstrates how political views, questionable as they are, can be legally expressed everywhere, without government interference. Conclusion Free speech and expression of political ideas are the very basis of a democratic system.As a fundamental feature of a democratic society, freedom of speech as it relates to politics is subject to only few, clearly defined restrictions. I believe that democracy demands that also those who have undemocratic views must be allowed to propagate for their ideas. A democratic state may only interfere with the right to express a political opinion if it can prove that the direct result of their speech would be violence and harm to somebody. Freedom of expression is a prerequisite for democracy and therefore without freedom of expression, there can be no democracy.This is why it continues to be important to facilitate healthy debates on this issue and help people understand why it is important to respect opinion of others, even if it is not in accordance with the mainstream. That is the best way to continue our rich democratic tradition and ensure that future generations can enjoy the same rights as we do. List of References Walker, Melissa. (2002) Unequal Freedom: How Race and Gender Shaped American Citizenship and Labor rev by Evelyn Nakano Glenn. Information retrieved on April 28th, 2008 from Website http://www.h-net. org/reviews/showrev. cgi? path=112431032792905 Gans, Judith. (2005). Citizenship in the Context of Globalization. Udall Center for Studies in Public Policy. Information retrieved on April 28th, 2008 from the Center Website ht tp://udallcenter. arizona. edu/programs/immigration/publications/Citizenship%20and%20Globalization. pdf Smith, E. S. (2003). What is The Bill of Rights Information retrieved on April 28, 2008 from Website http://www. wisegeek. com/what-is-the-bill-of-rights. htm? Bill of Rights Defense Committee. (2008).Current Treats to Freedom of Speech, Religion, and Assembly. Information retrieved on April 28, 2008 from Website http://www. bordc. org/threats/speech. php Hill, Kimberley. (2008). Threats against the Free Speech? The Campus World Information retrieved on April 28, 2008 from Campus World Website http://www. thecampusword. com/content/view/2264/593/ American Civil Liberties Union, ACLU. (1994) Hate Speech on Campus. Information retrieved on April 28, 2008 from Website http://www. aclu. org/studentsrights/expression/12808pub19941231. html

Technology Transfers Developing Renewable Energy Sources...

Technology Transfers: Putting Theory into Practice Climate change is an increasingly demanding issue as global population continues to grow, energy sources are being depleted and cooperation between actors to take action is often difficult to enforce. Renewable energy is a growing technology. With the depletion of fossil fuels as well as increased greenhouse gases in the atmosphere due to fossil fuel burning, energy dependency will have to shift to renewable technologies such as solar photovoltaic, wind, hydroelectric and geothermal. Unfortunately, these technologies are expensive and building new or altering old plants to allow for their use is costly. Because developing countries are in transition and have a growing energy demand,†¦show more content†¦These projects must transfer cleaner technology as well as foster sustainable development in Non Annex I countries. In Joint Implementation, both countries participating are committed to reductions under the Protocol (Cullet, 175). Flexible mechanisms lessen the financial burden of lowering emissions for Annex I countries and also involve developing nations in the international effort to reduce greenhouse gases in the atmosphere. Non- Annex I countries must be begin to adhere to the emission regulations of the Kyoto Protocol. In theory, technology transfers through Cleaner Development Mechanisms and Joint Implementations are an effective way to introduce cleaner technology, aiding both developing and developed countries; developing countries gain new knowledge and different techniques to shift their dependency away from nonrenewable energy sources and developed countries adhere to Kyoto provisions. This exchange is necessary and appears to be flawless, yet such transfers must be closely regulated to ensure the livelihoods of the people in developing nations rather than the economic benefits such actions will have for private corporations. Economic and social security must be granted to the developing countries in order for this mechanism to be followed and agreed upon. Technology transfers under the Kyoto Protocol further define the division between the North and the South and mayShow MoreRelatedRenewable Energy As A Means Of Reducing The Use Of Fossil Fuels1412 Words   |  6 Pagesdevelopments in renewable energy as a means of reducing the use of fossil fuels OUTLINE Thesis statement: benefits of renewable energy decreaseing the consumption of fossil fuels outweighs its disadvantages. Topic sentences: 1. First of all, renewable energy is more governable than nuclear power. 2. Furthermore, renewable energy is benefit to human in two ways, in particular environmentally friendly, and reducing the consumption of fossil fuels. 3. 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