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Disclaimer — This paper partially fulfills a writing requirement for first year (freshman) engineering students at the University of Pittsburgh Swanson School of Engineering. This paper is a student, not a professional, paper. This paper is based on publicly available information and may not be provide complete analyses of all relevant data. If this paper is used for any purpose other than these authors’ partial fulfillment of a writing requirement for first year (freshman) engineering students at the University of Pittsburgh Swanson School of Engineering, the user does so at his or her own risk.

GRAPHICAL PROCESSING UNIT ADVANCEMENTS FOR VIRTUAL SPACE RENDERING

Max Zeeman, maz55@pitt.edu, Lora 3:00; Adam Granieri, adg88@pitt.edu, Lora 1:00


Abstract Imagine having to solve the problem 1+1, and similar elementary math problems. Now imagine having to solve that same problem a million time overs. It would take the quickest writer or mathematician days to solve even the simplest problem a million times over. However, if you had thousands of quick mathematicians working with you, it would be possible to solve a million 1+1 problems in a few short minutes. This is essentially how a Graphical Processing Unit (GPU) functions, except in place of fast mathematicians, you have thousands of little cores that do similar processes.  A GPU’s classical primary function is to render three dimensional environments, which essentially can be summed up as an enormous series of basic problems. Our research would focus on the hardware advancements in GPU’s that have allowed them to become the computational powerhouses they are today. Specifically, we plan to examine the development of memory interfaces including GDDR5X (double data rate type five synchronous graphics random access memory), HBM (high bandwidth memory), and their subsequent influence on energy efficiency and power computing. Each memory type functions in entirely different ways, and each with its respective pros and cons.  This paper will focus on how these advancements have helped benefit sustainability in various industries, including cloud services, animation, and academia, such as mathematical and physics related theoretical calculations.

Key Words HBM, GDDR5X, Graphical Processing Unit, Memory Bus Interface, Parallel Processing

AN OVERVIEW OF GRAPHICAL PROCESSING UNITS

Graphical Processing Units (GPUs) do exactly as their namesake suggests; they are electronics dedicated to the computing of graphical related processes. This is a task that usually comes in the form of a myriad of algebraic equations, as GPUs are specifically designed to solve at boggling speeds. A GPU’s ability to solve algebraic equations and algorithms proves very useful in a computer system, as this can allocate more computation-related tasks away from the CPU, consequently making a computer system more efficient [1].

GPUs are composed of a massive parallel core architecture [1]. By arranging thousands of small efficient cores in this parallel structure, GPUs are capable of immense number crunching and multi-processing. This allows GPUs to be processing powerhouses that can do millions upon millions of calculations, and consequently, allow consumers to have amazing animated movies, games and other applications [1][2]. However, our analysis focuses on a deeper level of GPU functions, specifically that of the memory protocols of a GPU.

Although GPUs can do millions of calculations a second, GPUs can be limited by how quickly data is presented to and moved from the processing unit. This is where graphical memory takes a role. In an unconventional sense, you can imagine the calculating bottleneck like this; Louie Armstrong is wailing away on his trumpet, going through jazz scales, and blasting an amazing solo. At his level, Louie’s only limit holding him back is his breathing and airflow, not the speed or dexterity of his fingers as he plays. This can be translated back to graphical memory; in the context of this paper, it is not the speed at which data is processed that matters as much as how fast the data can be moved. HBM and GDDR5X are proving to be the two competing standards in memory bus technology. The purpose of this paper is to explore graphical memory bus interfaces, including HBM and GDDR5X, and to analyze how memory can store and relay data to the GPU, and overall benefit society.



THE GPU’S ROLE IN CURRENT TECHNOLOGICAL SYSTEMS

GPUs Compared to CPUs

A common misconception is that a GPU is no different from a CPU, the Central Processing Unit. While GPUs are still a type of processing unit, they are dedicated to the task of controlling what you can see on your monitor screen. CPUs on the other hand, handle all the other data related to making a computer work [3]. For example, CPUs have to execute the code to run your Mac or Windows operating system. GPUs in this scenario would execute the code that deals with the User Interface facets of your operating system, i.e. your login or menu screen.

The other notable difference is the type of processing cores each contains. CPUs normally contain 1, 2 or 4 processing core, versus GPUs, which can contain thousands. Similarly, both systems have an amazing amount of programmability, as to allow users to specify what each core (or in the GPU’s case, group of cores) should be tasked to do. In fact, GPU cores work most effectively if working in ‘parallel,’ and can thus handle multiple task simultaneously [1]. Although CPUs use to have to handle all calculations and related such task in the computer, “GPU-accelerated computing [now] offloads compute-intensive portions of the application to the GPU” [1]. This allows GPUs to handle the more compute related tasks that could slow down the CPU, and thus, lead to a more effective system overall. Also, in both processing units’ cases, CPUs and GPUs need a place to store and access data; this comes in the form of Random Access Memory and Graphical Random Access Memory [4].

MEMORY BUS INTERFACES

Memory Utilization

A memory bus is a protocol the computer uses to communicate digital and analog data and commands to system memory. The memory it communicates to is either the system Random Access Memory (RAM) or what is generally called the Graphical Random Access Memory (G-RAM) [4]. Data signals are sent and allocated from the CPU to the GPU for specific computations, almost exclusively for displaying images to the monitor. Hence the memory is allocated for calculating and combining different aspects of an image like color and placement [2]. When it comes to rendering a 3-dimensional space, the card must also account for shading, draw distance and different algorithms for enhancing an image [2]. The memory bus receives these commands and relevant data and distributes it to relevant memory modules and the computations to the processor. There the final image is assembled and sent through the display ports.

The memory bus can differ considerably on how it interfaces with the graphics card and the rest of the system, but all different protocols use the same basic structure of memory lanes, each with different bit-rates [4]. Most memory bus lanes are either 64 or 128 bit. In the following section, we will discuss what the memory and processors on the GPU are used for.

GPU memory functions

A memory bus is fundamentally a series of parallel paths for signals and subsequent data to travel from one component in the system to another or multiple others. Most often they are used to convert and transfer data from the central processing unit to the system memory [4]. In the case of GPUs, the memory bus takes tasks and data allocated to the GPU from the CPU, usually for a series of computationally heavy tasks like image assembly and rendering. The memory bus allocates the tasks and resources necessary for the image and computation from the CPU and system memory to the memory controllers and modules. The modules send the commands to the cache and related processing clusters. The protocol of the memory bus utilizes the Peripheral Component Interconnect express (PCIe) port interface to transfer and allocate the data. In the case for rendering applications, the memory bus distributes models and rigging to select memory modules as in figure 1 [5].



http://www.hpcresearch.nl/euroben/overview/web11/fermi.jpg

FIGURE 1 [5]
GPU Memory Workflow Diagram

Others would contain texture images and mapping for the desired model. The structure of the memory bus has a large impact on the speed of rendering and can in some cases, lead to a redesign of a GPU’s organization and pcb to optimize for efficiency and speed. Memory busses have two major performance metrics: bandwidth, or transfer speed, and clock speed, or transfer frequency. Bandwidth is usually measured in gigabytes per second (Gb/s) and clock speed in megahertz (MHz).



GDDR5X

Its design is a small iterative change from the previous generation of GDDR5 which was very large improvement in per pin data rate than GDDR4 as seen in figure 2. GDDR5 had an improvement of 5 Gb/s/pin over the previous generation. 7495083-fig-1-small



FIGURE 2 [4]

Memory Speed Over Successive Generations
In comparison GDDR5X had only an improvement of about 4 Gb/s/pin over GDDR5 [4]. The improvement from the most recent iteration form the previous can be attributed primarily to the addition of the PCIe 3.0 port becoming common place on consumer grade motherboards. The 3.0 port allows for a maximum transfer rate of 8 Giga-transfers per second per lane and an increase of 16 lanes over PCIe 2.0’s 8 lanes at 4 Giga-transfers per second [5].

7495083-fig-16-large

FIGURE 3 [4]

Memory Configuration of GDDR5 versus HBM
The GDDR5X protocol utilizes a standard structure for distribution of memory resources to the main processing module. The memory modules form a circle as seen in figure 3. With this configuration, innovation was more straightforward and less novel where the primary increase in performance is the improvements in processor and memory density. The smaller design allowed for more modules on each iteration [5]. The protocol itself distributes commands and assets to the memory modules simultaneously in a two-dimensional array, as the arrangement implies. It is limited in this aspect. This configuration cannot implement stacking for memory modules to allow parallel delivery [6]. From there, as seen in figure 1, memory goes to the common cache, them to processing clusters. The consequence of this is that GDDR5X performs well when it comes to tasks that aren’t heavily resource dependent and favor frequency over many simultaneous calculations. An example is in gaming, where there is a finite model and textures constrained in one environment. A finite model is one such that the shape and joints of movement are pre-defined or pre-programmed, instead of dynamic where the model can drastically change shape and functionally during playtime. It is similar with textures where the actual picture is already designed and mapped in a certain orientation on an object, it only needs to be rendered. Often there is a lot of simulated physics interactions and dynamic changing to the immediate environment. Hence the higher clock speed is generally favored to refresh the image more often.

HBM

Developed by semiconductor company, Advanced Micro Devices (AMD), High Bandwidth Memory (HBM) is quickly becoming the primary rival of GDDR5X. To make graphics memory more energy efficient, AMD engineers designed HBM to have vertically stacked memory chips, compared to GDDR5X’s more spread out memory. As can be seen in figure 2, HBM is composed of a stack of memory DRAM Dies that “interconnected by wires called “through-silicon vias,” or TSVs” [6] that are connected to an interposer and package substrate electrical interfaces.



hbm\'s processing architecture



FIGURE 4 [7]

HBM Memory Design
The interposer is essentially a spread out electrical circuit that connects various HBM die stacks to one another, as well as to the main GPU die for quick information transfer. The underlying package substrate acts as the circuit board [6]. In short, these electronics allows for an ultra-wide communication lanes with high energy efficiency.

Because of HBM’s vertically stacked memory structure, it is far denser for memory with a nearly 66% smaller footprint compared to GDDR5X according to figure 2. It is also important to note than the memory stacks can be expanded to a larger pcb, like GDDR5X’s configuration as well. What this means is a possibility for exponentially increased memory capacity if the layout is set to equal the physical footprint of GDDR5X. [7]

With the GPU products starting to come standard with HBM 2, the bandwidth gap between GDDR5X and HBM is likely to decrease. With the latest iteration of HBM, each memory die is now going to hold 8 GB of memory and have around 256 GB/s of bandwidth, compared to HBM’s 2 GB per DRAM die and 128GB/s bandwidth [6]. However, with these great steps in speed and efficiency comes great monetary cost to the user. Overall, computer users would stand to gain a more compact memory system that will eventually rival GDDR5X in terms of bandwidth speed and latency.

Contrasting HBM to GDDR5X

The main advantage of HBM is its power efficiency to bandwidth ratio. As a reminder, bandwidth is the speed at which information is transferred from one memory die stack to the GPU, and vice versa. Bandwidth transfer is normally measured in units of gigabytes per second (GB/s). Although GDDR5X has faster bandwidth and memory latency speeds compared to HBM, GDDR5X is held down by its lack of power efficiency, and as consequence, it could impede the development of GPU technology [6]. HBM conversely is a smaller, more compact memory chip that has a bandwidth ratio of up to 35 GB/s for every watt of power used, compared to GDDR5X’s 11 GB/s for every watt used [8]. However, an issue concerning the first iteration of HBM memory tends to run hot, as compared to GDDR5X. In a product review of the AMD R9 Nano 4GB, tester Rikki Wright found that the graphics card had a heat fluctuation of around 15 degrees Celsius, which is considered dangerous for a GPU [9]. They found the graphics card performed particularly poorly when used in SLI, which is being able to link two graphics cards together for better performance. In figure 5, Wright compares the R9 Nano to other GPUs in terms of temperature under load. https://scontent-iad3-1.xx.fbcdn.net/v/t34.0-12/17093953_1216034298515130_1872490116_n.jpg?oh=716e0fa1ddf79212b0b585dabfec9d6e&oe=58baf759


FIGURE 5 [9]

Temperature Comparison of the HBM R9 Graphics Cards versus GDDR5X Graphics Cards
Nonetheless, in today’s market, GDDR5X still has its cost advantages. Although its DRAM is not stacked like HBM, and are instead spread out evenly on the interposer, it is by far the quicker memory type as of now, and has not reached its energy limit yet. Where GDDR5X has speeds of 12 GB/s bandwidth per pin, HBM has only 128 GB/s per cluster of memory. This makes GDDR5X still a viable memory for both businesses and individual consumers alike, as it is by far the cheaper memory [10]. However, spatially speaking, HBM has the higher ground. HBM, being a three-dimensional memory made of stacks of DRAM dies, only takes 55 by 55 nanometers of space, versus that of GDDR5X, which is more spread out across the GPU, at 110 by 90 nanometers [4]. Overall, it becomes more of a limit of how much money a business or an individual can spend, the immediate cheaper solution being GDDR5X and the more expensive, but more efficient option being HBM.

SUSTAINABILITY FOR INDUSTRY AND ACADEMIA

What is Sustainability for GPUs?

In the case of GPUs, the question of sustainability is not one of ethics, but one of quality of life. What will this new technology do to improve existing human systems, or how will it create new, better systems? That is the question electrical and computer engineers must ask when designing a new piece of hardware, such as the discussed HBM or GDDR5X GPU memory. Improved GPU memory has a myriad of applications; this paper can only reach the beginning memory improving the quality of life. Thus, we decided to delve into a few examples of GPU memory’s usage in industry and academia, examining the technology’s influence in topics like entertainment, cloud-computing, and chemistry.



Implications for Industry

In terms of sustainability, GPUs help improve the quality of life, particularly in the business of entertainment. The most well-known application of GPU’s is rendering 3D spaces and images for entertainment. As discussed in a previous section, current GDDR5X graphics cards are generally favored in gaming applications and real-time rendering due to their higher clock-speeds and faster single lane data-transfer rates. For this reason, Nvidia, a company that only produces GDDR5X based cards had about 70% market share back in Q2 of 2016, while Advanced Micro Devices (AMD), the only company to commercially produce HBM based-cards had the remaining 30% [6]. In contrast to this, HBM is becoming increasingly popular in commercial rendering for movies and similar animated films. Disney, for one of their recent films, Big Hero 6, developed a new rendering engine called Hyperion. It was needed as the film has many scenes flying through a city-scape with many glass walls. This meant they had to render nearly the whole city with reflections and billions of light ray calculations in order get a few frames. The new engine benefits from parallel computation immensely. It algorithmically groups similar rays with direction and length into packets and sends them simultaneously to the GPU for computation [2]. Because this algorithm creates larger packets deliverable to the GPU, it directly benefits from the more parallel structure HBM provides. Although the lower clock speed reduces the frequency of calculations done, the larger bandwidth allows for more calculations in a shorter amount of time. The multi-GPU array scaling benefits as well. The larger amount of GRAM available also means either they can reduce the number of GPU’s needed to complete the render in the same amount of time as an array of GDDR5x based cards. This can allow the studios to devote more resources to create new techniques for simulating and rendering virtual spaces with less regard for computing times.

Sustainability also applies to companies wish to become more efficient, and thus, more “sustainable.” Relational database management systems (RDBMS) are another structure that benefit from GPUs and their capability. Compared to CPUs, GPUs and their high bandwidth memory prove useful for such things as database processing for businesses. Author Samuel Cremer in his paper on the “Efficiency of GPUs for Relational Database Engine Processing” describes how, “contain energy growing needs, numerous researches show that GPUs are more efficient than CPUs for high and intensive computing” [11]. The parallel functionality of GPUs cores proves useful, and can handle large vectorized data processes. Also, compared to CPU Random Accesses Memory, GPU GRAM has nearly 10 times the bandwidth speed [11]. These facets allow GPUs to outperform CPUs in RDBMS in almost every area, except in a few, very specific ways.

Cloud-computing has become a popular buzz-word and equally as ubiquitous. In fact, Amazon’s Cloud Services division has its largest by far, generating nearly $13 billion last year and holding over 30% of cloud services market [7]. Amazon Web Services are the warehouses of server arrays that Amazon uses for hosting its website and renting use to third-parties. Currently, a customer may rent-out however many clusters, which are just a collection of CPUs and GPUs and send them instructions to perform some computation for a certain amount of time. Some businesses will run market simulations for future investments or render a video where they do not have the resources locally to do so [11]. Since the range of tasks is so broad, HBM is not very widely used, since it only shines in asset-heavy workloads. Though with future iterations, it could free up server space by a considerable factor thanks to smaller pcb foot print and vertical stacking of memory modules, meaning more dense warehouses and more widely available, cheaper cloud computing services.



Benefit for Fields of Academia

Besides benefiting industries like Amazon and Disney, new high bandwidth memory in GPUs are also proving invaluable by improving sustainability in various fields of academia, including mathematics, physics, and chemistry. Advancements in graphics memory have allowed these fields to simulate previously arduous models in topics like non-linear physics or quantum chemistry. However, of the two studies, the chemistry study should be taken with reservations, as it took place in 2009, which is out of the period of the discussed memory types.

For his Master’s, electrical engineer Shenhao Yan writes about how power electronics can be utilized to complete accurate and efficient simulations for non-linear physics based modeling. Up until this point, “due to model complexity and nonlinear device characteristics, the application of physics-based model has hitherto been limited” [12]. Thus, the advent of the massively multi-core processing has proven itself invaluable. Yan asserts that for numerical solvers for matrices, such as Gaussian Elimination and Jacobian Blocks, that GPUs help to bring admirable computation capability [12]. He hopes that this will lead to an increase of usage of massively parallel simulation, that can take full advantage of GPU capabilities, and thus boost the research of mathematical and physics-related simulations.

Another field of academia that has been positively affected by GPUs is chemistry. In the Journal of Chemistry, the article, Quantum Chemistry on Graphical Processing Units, by Ivan Ufimtsev and Todd Martinez describes how recent advances in GPU technology and accessibility have made in possible to “increase the number of publications in different fields, such as classical molecular dynamics and quantum chemistry’” [13]. Ufmitsev and Martinez goes so far as to claim that a ‘video gaming machine’ can outpace even the highest end quad-core workstation computer when it comes to processing energy and gradient calculations of different organic molecules.

After testing a gaming computer containing two Nvidia graphics cards running parallel versus an Intel quadcore workspace computer, they found that the computer containing the two Nvidia GPUs performed significantly faster. For small molecules, both machines completed the energy and gradient calculations at about the same pace [13]. However, for medium-size molecules the speedup range[d] between 20× and 25×, while for large molecules it exceed[ed] 100× [9]. To give context, for the molecule olestra, the time it took for the CPU system to computation of the energy and gradient was about 6 hours, versus that of the GPU systems, which was a little over two minutes.

To reiterate, this study should be taken with a grain of salt, as it took place in 2009, before the discussed graphical memory interfaces HBM and GDDR5X were even created. However, considering the increased computational speeds using just two GPUs meant for gaming, we can extrapolate that our two GPU memories of interest could only help increase the computational speeds and efficiency of this quantum chemistry research.


WHAT’S AHEAD FOR GPU MEMORY AND SUSTAINABILITY

Cost of HBM

The major predicament that’s keeping HBM from dethroning GDDR5X is the sheer price gap between the two competing memories. Most recently, NVIDIA has revealed their own take on HBM memory, in the form of their Pascal memory architecture, for their upcoming line of Quadro graphics cards [14]. However, graphics cards like the Quadro P6000 cost upwards of $5000, which is most certainly not a feasible option for the average consumer. NVIDIA is pushing their line of HBM cards for pure work-system and CAD systems, not particularly for the casual gamer. AMD similarly just announced its own line of HBM graphics cards, albeit more geared towards average consumers in terms of price [15]. However, as newer iterations of HBM memory are released by these competing companies in the form of HBM 2, the price and power of these cards will continue to rise, while still staying power efficient. Until this happens, GDDR5X will remain the go to memory type of GPUs.



Accessibility and Sustainability

Price sustainability is a very important factor that determines whether a product will allow a company to turn a profit. If no consumers, corporations, or universities invested in HBM, companies like Nvidia and AMD would likely discontinue the technology. However, this is simply not the case. HBM may be expensive, but it was able to sell itself well enough to allow these companies to invest and improve the technology. As mentioned previously, Nvidia recently released their own HBM 2.0 with their Pascal series of graphics cards, which perform just as well as their GDDR5X counterparts [15]. AMD is successfully selling consumer grade versions of the cards that are less than $1000 [14]. HBM is not a technological fad; it is set to be a true advancement for graphics cards that is sustainable for everyone involved, whether it be the company designing the card, or the industry that buys it.



Single Channel HBM

The unfortunate drawback with HBM so early on in its development is its lack of single-channel data transfer relative to GDDR5X [5]. As a goal of the development of HBM at AMD was to create vastly superior simultaneously data transfer, there was a compromise made to allow access to memory module at the same time. This compromise rendered it handicapped in gaming, which is what most consumer GPU’s are sold for. Hence AMD’s R9 Fury X did not perform as well hoped compared to competitors and ran so hot they sold it with a built-on water cooling apparatus instead of a traditional air cooler. An improvement in single channel performance would reduce the strain on the processing cluster and allow for lower clock-speeds to achieve the same performance, which in turns means lower temperatures in most consumer workloads. Going forward, that will be the biggest improvement consumers and businesses will be looking for to make HBM more ubiquitous.



The Final Word

As of right now, GDDR5X will remain the preferable memory type, for its single lane data transfer speeds and cost alone. It performs sufficiently enough for consumer applications like gaming and content creation in the mean while. HBM, given time, will eventually overtake GDDR5X in terms of power and efficiency, but currently, as still yet to reach this goal. Nonetheless, HBM still must jump through the monetary hoop to be relevant to the average consumer, as it is unlikely that the average consumer will drop $5000 dollars for a graphics card, no matter how efficient it may be. However, if GDDR5X does not have a drastic iteration, it will likely be phased out by HBM within the next decade, leading to the most energy efficient graphics memory to date for consumers and businesses alike.


SOURCES CITED

[1] “What is GPU Accelerated Computing?” Nvidia. 2017. http://www.nvidia.com/object/what-is-gpu-computing.html

[2] “Disney's Hyperion Renderer.” Walt Disney Animation Studios. 2016.

https://www.disneyanimation.com/technology/innovations/hyperion

[3] J. Ghorpade. “An Introduction to Graphical Processing Unit.” IJMER. 2011. Accessed 2.20.2017.

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.416.5517&rep=rep1&type=pdf

[3] “What is Cloud Computing?”. Amazon Web Services. 2016.

https://aws.amazon.com/what-is-cloud-computing/

[4]  C. Kim. “Memory Interfaces: Past, Present, and Future.” IEEE Solid-State Circuits Magazine. 2012.

http://ieeexplore.ieee.org/xpls/icp.jsp?arnumber=7495083&tag=1

[5] J. Ajanovic. “PCI Express (PCIe) 3.0 Accelerator Features.” Intel Corp. 2008. Accessed 2.25.2017.

http://www.thailand.intel.com/content/dam/doc/white-paper/pci-express3-accelerator-white-paper.pdf

[6] K. Jungrae. “All-Inclusive ECC: Thorough End-to-End Protection for Reliable Computer Memory.” 43rd Annual International Symposium on Computer Architecture (ISCA). 2016.

http://ieeexplore.ieee.org/abstract/document/7551427/

[7] “High Bandwidth Memory, Reinventing Memory Technology.” AMD. 2015. Accessed 2.21.2017

http://www.amd.com/en-us/innovations/software-technologies/hbm

[8] A. Shilov. “Discrete Desktop GPU Market Trends Q2 2016: AMD Grabs Market Share, but NVDIA Remains on Top.” AnandTech. 9.13.2016. Accessed 2.25.2017.

http://www.anandtech.com/show/10613/discrete-desktop-gpu-market-trends-q2-2016-amd-grabs-market-share-but-nvidia-remains-on-top

[9] R. Wright. “AMD R9 Nano 4GB (HBMv1) CrossFire Review.” eTeknix. 2016. Accessed 2.28.2017

http://www.eteknix.com/amd-r9-nano-4gb-hbmv1-crossfire-review/

[10] “Amazon Web Services: 2016 In Review.” Forbes. 12.29.2016. Accessed 2.25.2017

https://www.forbes.com/sites/greatspeculations/2016/12/29/amazon-web-services-2016-in-review/

[11] S. Cremer. “Efficiency of GPUs for Relational Database Engine Processing.” International Conference on Algorithms and Architectures for Parallel Processing. 2016. Accessed 1.15.2017

http://link.springer.com/chapter/10.1007/978-3-319-49956-7_18

[12] S. Yan. “Large-Scale Power Electronic Circuit Simulation on a Massively Parallel Architecture.” Education and Research Archive of the University of Alberta. 2016. Accessed 1.15.2017

https://era.library.ualberta.ca/files/c348

[13] I. Ufmitsev. “Quantum Chemistry on Graphical Processing Units. 3. Analytical Energy Gradients, Geometry Optimization, and First Principles Molecular Dynamics.” Journal of Chemical Theory and Computation. 2009. Accessed 2.20.2017

http://pubs.acs.org/doi/pdf/10.1021/ct9003004

[14] “AMD Radeon R9 Series Gaming Graphics Cards with High-Bandwidth Memory.” AMD. 2017. Accessed 2.22.2017

http://www.amd.com/en-us/products/graphics/desktop/r9

[15] R. Smith. “NVIDIA Announces Quadro GP100 – Big Pascal Comes to Workstations.” AnandTech. 2.5.2017. Accessed 2.20.2017

http://www.anandtech.com/show/11102/nvidia-announces-quadro-gp100


ACKNOWLEDGMENTS

A man once said to me, “Knowledge is the ultimate form of power.” That man was Tim Cibos, and he is a fellow resident on floor 5 of Forbes Hall here at the University of Pittsburgh. Tim is from a small town in Central Pennsylvania, and has been an inspiration to us through the whole process. His academic integrity, grit and devotion have been incredibly inspiring over the course of this paper. He supported both of us by providing intellectual support and being a good person to bounce ideas and writing quality off of. Similarly, Glenn Louis Mursky has also been a source of emotional support through this difficult writing process. His kind words have gotten through the thick and thin. We would like to thank our writing instructor, Tim Maddocks and our Co-Chair, Nick Haver for helping us through learning the process of writing a research paper. We would also like to thank Floor 5 of Forbes Hall in general for giving feedback on our paper topic and being the genuinely best people we have had the pleasure of working with. We wish them the best on all of their papers as well.








University of Pittsburgh Swanson School of Engineering 1

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