First Asian Himalayas International Conference on Internet AH-ICI2009 Hyatt Regency Kathmandu, KATHMUNDU, NEPAL 3- 5th of November, 2009
Multi-Scale Modeling of Nano Scale Phenomenon using CUDA based HPC Setup Rohit Pathak╫ and Satyadhar Joshi┼ ╫ ┼
Acropolis Institute of Technology & Research, Indore, Madhya Pradesh, India Shri Vaishnav Institute of Technology & Science, Indore, Madhya Pradesh, India
[email protected],
[email protected]
Abstract-The essence of High performance computing (HPC) in the field of computation Nanotechnology and problems encountered by HPC arrangement in applying HPC to Nanoenabled calculations have been presented in the paper. A proposal to optimize computations in an HPC setup has been formulated to make Nanotechnology computations more effective and realistic on a CUDA based framework. Results and findings in the expected setup and the computation complexities that will be needed in its implementation have been suggested with an algorithm to take advantage of inbuilt powerful parallelization capabilities of GPU making large scale simulation possible. Implementation of CUDA in certain complex techniques in Nanotechnology is presented with a significant improvement in performance as compared to the last work which was implemented using distributive computing toolbox in MATLAB. We have discussed about the problems that exist and how we can optimize the computations in a HPC setup and how we can make use of computational power of GPU to make Nanotechnology computations more effective and realistic. A description of the progress in this area of research, future works and a probable extension is proposed.
N
I. INTRODUCTION
anotechnology is the realization and engineering of matter at dimensions of roughly 1 to 100 nanometers, where unique phenomena enable novel applications. Encompassing nano-scale science, engineering and technology with an involvement of nanotechnology in imaging, measuring, modeling, and manipulating matter at this length scale. Computation, modeling and simulation today play an equal role to theory and physical experimentation in discovery-driven engineering research [5]. Using the most advanced high-performance computing resources and a well worked out algorithm for innovating technology and reducing design-cycle time and reliability [7]. Compiling advanced calculations on Carbon Nanotube (CNT) [6], Microelectromechanical systems (MEMS) and Nanofabrication and computations on characterization of CNT, calculation of various properties of CNT, integration of CNT with MEMS, nanocomposites of CNT and reliability of CNT based devices which need advanced calculations has been worked out in this paper. Introduction of a single atom or molecule in the chemical structure of CNT can change the entire configuration of the device manufactured from nano-materials. Incessant updates in existing theories in each of these areas make the study of computational Nanotechnology more arduous and
demanding as persistent revision of knowledge in the domain of nanotechnology has become mandatory. At present the most used software solutions available are MATLAB [1] and Coventorware [4] but they do not cover all the new advancements and progressions taking place in the field of Nanotechnology as it is a rapidly evolving field. On Micro-scale software like Coventorware based on MEMS, it requires high computational power and if we add multi-scale modeling, characterization and reliability as parameters then the need for higher performance is still more eminent. Nanotechnology is a highly advanced science with many potential applications. Its impact is already being felt in materials engineering, electronics, medicine and other scientific disciplines. Current research in nanotechnology requires multi-disciplinary knowledge, not only in the sciences and engineering domain but also in the high performance computing (HPC) technology. Many nano-science explorations rely on established, efficient HPC and computational algorithms, practical and reliable numerical methods and large-scale computing systems. In our previous operations we have been working on advanced calculations on Carbon Nanotube, MEMS, Nano fabrications [1, 2, 13, 14], and we have shown how reliability computations can benefit from HPC with MATLAB [1], MCCS [2], and various other environments, each of them having their pros and cons [3]. For example work such as characterization of CNT, calculations of various properties of CNT, integration of CNT with MEMS (Micro Electro Mechanical System), nanocomposites of CNT, reliability of CNT based devices needs advanced calculations. This is because a single atom can change the entire configuration of the device manufactured from Nanomaterials. Continuous updates and new theories in each of these areas make the application Nanotechnology more difficult. The main thing we need to work from here is on “multiscale modeling and simulation” because from the macro to nano phenomenon everything is linked so we need high computation power to work phenomenon’s we are aware in all the intermediate scale that exists from macro to nano. The algorithm we are planning will work and breakdown the problem statement in a way so that we can distribute the computation effectively in various clusters of a HPC system.
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First Asian Himalayas International Conference on Internet AH-ICI2009 Hyatt Regency Kathmandu, KATHMUNDU, NEPAL 3- 5th of November, 2009
The best example that can be stated is a CNT based complex computations, which clearly depicts the complexities involved in doing such kind of computations, and shows how parallelization is important in such computations. Thus by using optimized algorithms for these calculations we can successfully make computation optimized for HPC and make things easy in Nanotechnology and related domains. II.
Scale
Properties
Macro Level Input Stage/Problem
Thermal Effects
MULTISCALE MODELING & SIMULATION
Electrical Effects
Computation for Molecular Dynamics
The calculations are distributed in 4 categories as shown in Fig.1.
Chemical Effects Computations for Semi Quantum Level
Quantum Effects (Most complex)
Atomic Effects
Magnetic Effects
Fig. 2. Various Computations
Fig.1. Division of various Computational Domains
The proper linking of different properties at different level allows us to accurately predict phenomenon’s that were prior inexplicable in current models of studies. For example in [10] author has demonstrated physical models elucidating several facets of device degradation at the nanoscale. It has been substantiated that various qualitative differences must be taken into consideration as devices for scaling of devices into the nano realm. The computations required can be exemplified by these two formulae that follow. Various developments in Nanotech are only fruitful if they are leading to highly reliable devices, because reliability is an area which is expected to benefit the most from multiscale modeling. In the same area a simplified version of the percolation model [8, 9] for nanoscale device damage modeling gives us a failure function of the form Aax
§ · a2 F (t ) 1 ¨1 f (t ) ¸ © ¹ tox a
Where,
f (t )
is the defect density generated in block of
t
A
dimension a , ox and ax are the oxide thickness and area respectively. And, the rate of defect creation for nano-scale devices has been calculated [10] assuming the defect creation events are independent and that single electrons are
responsible for a bond-breaking event. The rate equation for defect creation is of the first order in the number of defects and its solution is given as:
§t· N (t ) 1 exp ¨ ¸ ©W ¹ Where, N is the number of defects and W is the lifetime for the creation of a defect. The above formulae explicate the need for HPC which needs to be optimized with multi scale modeling. Modeling of materials and devices can be done using the modeling library, simulate them using the simulation library, and then we can compute the reliability of the device. The reliability depends upon many parameters such as environmental conditions etc. and the library will calculate and analyze the reliability for the provided parameters and specifications of the device. Also in [12] quantum realm we have the following examples to expound our modus operandi. As a particular example, the
\
Q quantum correction potential can be articulated as a simple analytical function of the distance z from the surface and given as
\Q
§b ©
1·
Eb¨ ¸ 4 z ¹
First Asian Himalayas International Conference on Internet AH-ICI2009 Hyatt Regency Kathmandu, KATHMUNDU, NEPAL 3- 5th of November, 2009
Input Data or Requirement or Problem Statement
Multiscale breakdown and parameters for various domains of the Input
Complex Calculations from the main Computation 1 which decides the distribution and verifications of parameters
Computation 2 for Nano Domain computations, Quantum effects, Nano mechanics characterization and reliability
No
Computation 3 for Micro and intermediate computations, like molecular dynamics, thermodynamics, and electrodynamics
Synchronizing of Results and output
Fig. 3. Expected Setup
Yes
1/3
§ 12q 2 m* § 11 ·· b ¨ ¨ N depl Ninv ¸ ¸ 2 32 ¹ ¹ and the terms in © H= © where
b are
defined as,
q is
the elementary charge,
*
m
is the
electron effective mass, H is the dielectric constant of Si, the reduced Planck constant,
N depl
= is
is the sheet density of the
N
inv is the sheet fixed charges in the depletion region, and density of the inversion electrons. The energy gap for
semiconducting carbon nanotubes [11]
Egap
2
Ecc acc dCNT
Egap
is formulated as
where
dCNT is the carbon nanotube diameter, Ecc is the acc
carbon-to-carbon tight-binding overlap energy and nearest-neighbour carbon-to-carbon (
acc
0.142
is the distance
nm).
Model for elementary computation of elemetry level abstration are given as follows Electrostatic Potential Electrostatic potential is defined in terms of electric field E as:
IE
³ E dA C
First Asian Himalayas International Conference on Internet AH-ICI2009 Hyatt Regency Kathmandu, KATHMUNDU, NEPAL 3- 5th of November, 2009
Data and Problem Division Discreet Computations
Kinetic
Continuum
Theory
Theory Quantum
Molecular
Mechanics
Dynamics
SIMT execution
Synchronization
Fig. 4. Division of Computation
Analysis & Result
Where:
IE is
the electrostatic potential at the point under consideration, C is an arbitrary path connecting the point with zero potential to the point under consideration, and E is the magnitude of electric field at that point. Kinetic theory of gases Expression for the pressure
P
2 Nmvrms 3V
Where: N is the number of molecules, m is the molecular mass, vrms is the root-mean-square velocity of the collection of particles, and V is the volume of the gas.
CONCLUSION HPC can accelerate research in Nanotechnology by optimizing the distribution of computations and taking advantage of the recent developments in CUDA. The integration of other tools from MATLAB makes the complex Nano technological calculations easier to operate on, the execution is faster and there is lesser response time in getting the output result. Thus we have tried to illustrate a novel approach for Nanoscale Modeling and Computations in this regard which can lead to acceleration of work in this area. Connection and allocation of the problems in a CUDA based HPC setup and conceivable future developments have been explained elaborately. With the developments in multi scale modeling still at an early stage for nanotechnology based calculation these results can add to more innovation in computation nanotechnology.
First Asian Himalayas International Conference on Internet AH-ICI2009 Hyatt Regency Kathmandu, KATHMUNDU, NEPAL 3- 5th of November, 2009
Discreet Computations Grid 1 – Quantum Mechanics
Grid 2 – Molecular Dynamics
Block (0, 0)
Block (1, 0)
Block (2, 0)
Block (0, 0)
Block (1, 0)
Block (2, 0)
Block (0, 1)
Block (1, 1)
Block (2, 1)
Block (0, 1)
Block (1, 1)
Block (2, 1)
Grid 3 – Kinetic Theory
Grid 4 – Continuum Theory
Block (0, 0)
Block (1, 0)
Block (2, 0)
Block (0, 0)
Block (1, 0)
Block (2, 0)
Block (0, 1)
Block (1, 1)
Block (2, 1)
Block (0, 1)
Block (1, 1)
Block (2, 1)
Fig. 5. Discreet Computational Grids
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