Octree-based, GPU implementation of a continuous cellular automaton for the simulation of complex, evolving surfaces

Presently, dynamic surface-based models are required to contain increasingly larger numbers of points and to propagate them over longer time periods. For large numbers of surface points, the octree data structure can be used as a balance between low memory occupation and relatively rapid access to the stored data. For evolution rules that depend on neighborhood states, extended simulation periods can be obtained by using simplified atomistic propagation models, such as the Cellular Automata (CA). This method, however, has an intrinsic parallel updating nature and the corresponding simulations are highly inefficient when performed on classical Central Processing Units (CPUs), which are designed for the sequential execution of tasks. In this paper, a series of guidelines is presented for the efficient adaptation of octree-based, CA simulations of complex, evolving surfaces into massively parallel computing hardware. A Graphics Processing Unit (GPU) is used as a cost-efficient example of the parallel architectures. For the actual simulations, we consider the surface propagation during anisotropic wet chemical etching of silicon as a computationally challenging process with a wide-spread use in microengineering applications. A continuous CA model that is intrinsically parallel in nature is used for the time evolution. Our study strongly indicates that parallel computations of dynamically evolving surfaces simulated using CA methods are significantly benefited by the incorporation of octrees as support data structures, substantially decreasing the overall computational time and memory usage. © 2010 Elsevier B.V. All rights reserved.We thank the anonymous reviewers for their valuable comments and suggestions. This work has been supported by Programa de Becas de Excelencia de la Universidad Politecnica de Valencia (PAID-09-09), MEXT Grant in Aid Research (Kakenhi: Silicon etching (A) 19201026), and the Global COE program of Japan (GCOE, Wakate JSPS Young Scientist Fund).Ferrando Jódar, N.; Gosalvez, M.; Cerdá Boluda, J.; Gadea Gironés, R.; Sato, K. (2011). Octree-based, GPU implementation of a continuous cellular automaton for the simulation of complex, evolving surfaces. Computer Physics Communications. 182(3):628-640. https://doi.org/10.1016/j.cpc.2010.11.004S628640182

Automatic Loop Tuning and Memory Management for Stencil Computations

The Texas Instruments C66x Digital Signal Processor (DSP) is an embedded processor technology that is targeted at real time signal processing. It is also developed with a high potential to become the new generation of coprocessor technology for high performance embedded computing. Of particular interest is its performance for stencil computations, such as those found in signal processing and computer vision tasks. A stencil is a loop in which the output value is updated at each position of an array by taking a weighted function of its neighbors. Efficiently mapping stencil-based kernels to the C66x device presents two challenges. The first one is how to efficiently optimize loops in order to facilitate the usage of Single Instruction Multiple Data (SIMD) instructions. On this architecture, like most others, SIMD instructions are not directly generated by the compiler. The second problem is how to manage on-chip memory in a way that minimizes off-chip memory access. Although this could theoretically be achieved by using a highly associative cache, the high rate of data reuse in stencil loops causes a high conflict miss rate. One way to solve this problem is to configure the on-chip memory as a program controlled scratchpad. It allows user to buffer a 2D block of data and minimizes the off-chip data access. For this dissertation, we have accomplished two goals: (1) Develop a methodology for optimization of arbitrary 2D stencils that fully utilize SIMD instructions through microachitecture-aware loop unrolling. (2) Deliver an easy-to-use scratchpad buffer management system and use it to improve the memory efficiency for 2D stencils. We show in the results and analysis section that our stencil compiler is able to achieve up to 2x speed up compared with the code generated by the industrial standard compiler developed by Texas Instruments, and our memory management system is able to achieve up to 10x speed up compared with cache

Acceleration of split-field finite difference time-domain method for anisotropic media by means of graphics processing unit computing

The implementation of split-field finite difference time domain (SF-FDTD) applied to light-wave propagation through periodic media with arbitrary anisotropy method in graphics processing units (GPUs) is described. The SF-FDTD technique and the periodic boundary condition allow the consideration of a single period of the structure reducing the simulation grid. Nevertheless, the analysis of the anisotropic media implies considering all the electromagnetic field components and the use of complex notation. These aspects reduce the computational efficiency of the numerical method compared with the isotropic and nonperiodic implementation. Specifically, the implementation of the SF-FDTD in the Kepler family of GPUs of NVIDIA is presented. An analysis of the performance of this implementation is done, and several applications have been considered in order to estimate the possibilities provided by both the formalism and the implementation into GPU: binary phase gratings and twisted-nematic liquid crystal cells. Regarding the analysis of binary phase gratings, the validity of the scalar diffraction theory is evaluated by the comparison of the diffraction efficiencies predicted by SF-FDTD. The analysis for the second order of diffraction is extended, which is considered as a reference for the transmittance obtained by the SF-FDTD scheme for periodic media.This work was supported by the Ministerio de Economía y Competitividad of Spain under projects FIS2011-29803-C02-01 and FIS2011-29803-C02-02 and by the Generalitat Valenciana of Spain under projects PROMETEO/2011/021, ISIC/2012/013, and GV/2012/099

Memoria CFM 2011

N

An investigation of the efficient implementation of Cellular Automata on multi-core CPU and GPU hardware

Copyright © 2015 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Parallel and Distributed Computing . Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Parallel and Distributed Computing Vol. 77 (2015), DOI: 10.1016/j.jpdc.2014.10.011Cellular automata (CA) have proven to be excellent tools for the simulation of a wide variety of phenomena in the natural world. They are ideal candidates for acceleration with modern general purpose-graphical processing units (GPU/GPGPU) hardware that consists of large numbers of small, tightly-coupled processors. In this study the potential for speeding up CA execution using multi-core CPUs and GPUs is investigated and the scalability of doing so with respect to standard CA parameters such as lattice and neighbourhood sizes, number of states and generations is determined. Additionally the impact of ‘Activity’ (the number of ‘alive’ cells) within a given CA simulation is investigated in terms of both varying the random initial distribution levels of ‘alive’ cells, and via the use of novel state transition rules; where a change in the dynamics of these rules (i.e. the number of states) allows for the investigation of the variable complexity within.Engineering and Physical Sciences Research Council (EPSRC

Evolutionary continuous cellular automaton for the simulation of wet etching of quartz

Anisotropic wet chemical etching of quartz is a bulk micromachining process for the fabrication of micro-electro-mechanical systems (MEMS), such as resonators and temperature sensors. Despite the success of the continuous cellular automaton for the simulation of wet etching of silicon, the simulation of the same process for quartz has received little attention-especially from an atomistic perspective-resulting in a lack of accurate modeling tools. This paper analyzes the crystallographic structure of the main surface orientations of quartz and proposes a novel classification of the surface atoms as well as an evolutionary algorithm to determine suitable values for the corresponding atomistic removal rates. Not only does the presented evolutionary continuous cellular automaton reproduce the correct macroscopic etch rate distribution for quartz hemispheres, but it is also capable of performing fast and accurate 3D simulations of MEMS structures. This is shown by several comparisons between simulated and experimental results and, in particular, by a detailed, quantitative comparison for an extensive collection of trench profiles. © 2012 IOP Publishing Ltd.We are grateful to D Cheng and K Sato (Nagoya University, Japan) for providing part of the experimental data. We acknowledge support by the JAE-Doc grant form the Junta para la Ampliacion de Estudios program co-funded by FSE, the Ramon y Cajal Fellowship Program by the Spanish Ministry of Science and Innovation, NANO-IKER Project (IE11-304) from the ETORTEK program by the Basque Government and the Professor Partnership Program by NVIDIA Corporation.Ferrando Jódar, N.; Gosalvez Ayuso, MA.; Colom Palero, RJ. (2012). Evolutionary continuous cellular automaton for the simulation of wet etching of quartz. Journal of Micromechanics and Microengineering. 22(2). https://doi.org/10.1088/0960-1317/22/2/025021S222Hida, H., Shikida, M., Fukuzawa, K., Murakami, S., Sato, K., Asaumi, K., … Sato, K. (2008). Fabrication of a quartz tuning-fork probe with a sharp tip for AFM systems. Sensors and Actuators A: Physical, 148(1), 311-318. doi:10.1016/j.sna.2008.08.021Oh, H., Kim, G., Seo, H., Song, Y., Lee, K., & Yang, S. S. (2010). Fabrication of micro-lens array using quartz wet etching and polymer. Sensors and Actuators A: Physical, 164(1-2), 161-167. doi:10.1016/j.sna.2010.10.003Xing, Y., Gosálvez, M. A., & Sato, K. (2007). Step flow-based cellular automaton for the simulation of anisotropic etching of complex MEMS structures. New Journal of Physics, 9(12), 436-436. doi:10.1088/1367-2630/9/12/436Zhou, Z., Huang, Q., Li, W., & Deng, W. (2007). A cellular automaton-based simulator for silicon anisotropic etching processes considering high index planes. Journal of Micromechanics and Microengineering, 17(4), S38-S49. doi:10.1088/0960-1317/17/4/s03Gosalvez, M. A., Yan Xing, & Sato, K. (2008). Analytical Solution of the Continuous Cellular Automaton for Anisotropic Etching. Journal of Microelectromechanical Systems, 17(2), 410-431. doi:10.1109/jmems.2008.916339Zhou, Z., Huang, Q., & Li, W. (2009). Modeling and Simulations of Anisotropic Etching of Silicon in Alkaline Solutions with Experimental Verification. Journal of The Electrochemical Society, 156(2), F29. doi:10.1149/1.3031485Rangsten, P., Hedlund, C., Katardjiev, I. V., & Bäcklund, Y. (1998). Etch rates of crystallographic planes inZ-cut quartz - experiments and simulation. Journal of Micromechanics and Microengineering, 8(1), 1-6. doi:10.1088/0960-1317/8/1/001Tellier, C. R., & Leblois, T. G. (2000). Micromachining of quartz plates: determination of a database by combined stereographic analysis and 3-D simulation of etching shapes. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 47(5), 1204-1216. doi:10.1109/58.869067Hedlund, C., Lindberg, U., Bucht, U., & Soderkvist, J. (1993). Anisotropic etching of Z-cut quartz. Journal of Micromechanics and Microengineering, 3(2), 65-73. doi:10.1088/0960-1317/3/2/006Liang, J., Kohsaka, F., Matsuo, T., & Ueda, T. (2007). Wet Etched High Aspect Ratio Microstructures on Quartz for MEMS Applications. IEEJ Transactions on Sensors and Micromachines, 127(7), 337-342. doi:10.1541/ieejsmas.127.337Gosálvez, M. A., Xing, Y., Sato, K., & Nieminen, R. M. (2009). Discrete and continuous cellular automata for the simulation of propagating surfaces. Sensors and Actuators A: Physical, 155(1), 98-112. doi:10.1016/j.sna.2009.08.012Zhenjun Zhu, & Chang Liu. (2000). Micromachining process simulation using a continuous cellular automata method. Journal of Microelectromechanical Systems, 9(2), 252-261. doi:10.1109/84.846706Gosálvez, M. A., Xing, Y., Sato, K., & Nieminen, R. M. (2008). Atomistic methods for the simulation of evolving surfaces. Journal of Micromechanics and Microengineering, 18(5), 055029. doi:10.1088/0960-1317/18/5/055029Ferrando, N., Gosálvez, M. A., Cerdá, J., Gadea, R., & Sato, K. (2011). Octree-based, GPU implementation of a continuous cellular automaton for the simulation of complex, evolving surfaces. Computer Physics Communications, 182(3), 628-640. doi:10.1016/j.cpc.2010.11.004Mühlenbein, H., & Schlierkamp-Voosen, D. (1993). Predictive Models for the Breeder Genetic Algorithm I. Continuous Parameter Optimization. Evolutionary Computation, 1(1), 25-49. doi:10.1162/evco.1993.1.1.25Kohsaka, F., Liang, J., Matsuo, T., & Ueda, T. (2007). High Sensitive Tilt Sensor for Quartz Micromachining. IEEJ Transactions on Sensors and Micromachines, 127(10), 431-436. doi:10.1541/ieejsmas.127.43

Level set implementation for the simulation of anisotropic etching: application to complex MEMS micromachining

The use of atomistic methods, such as the continuous cellular automaton (CCA), is currently regarded as an accurate and efficient approach for the simulation of anisotropic etching in the development of micro-electro-mechanical systems (MEMS). However, whenever the targeted etching condition is modified (e. g. by changing the substrate material, etchant type, concentration and/or temperature) this approach requires performing a time-consuming recalibration of the full set of internal atomistic rates defined within the method. Based on the level set (LS) approach as an alternative and using the experimental data directly as input, we present a fully operational simulator that exhibits similar accuracy to the latest CCA models. The proposed simulator is tested by describing a wide range of silicon and quartz MEMS structures obtained in different etchants through complex processes, including double-sided etching as well as different mask patterns during different etching steps and/or simultaneous masking materials on different regions of the substrate. The results demonstrate that the LS method is able to simulate anisotropic etching for complex MEMS processes with similar computational times and accuracy as the atomistic models.This work has been supported by the Spanish FPI-MICINN BES-2011-045940 grant and the Ramon y Cajal Fellowship Program by the Spanish Ministry of Science and Innovation. Also, we acknowledge support by the JAE-Doc grant from the Junta para la Ampliacion de Estudios program co-funded by FSE and the Professor Partnership Program by NVIDIA Corporation.Montoliu, C.; Ferrando Jódar, N.; Gosalvez Ayuso, MA.; Cerdá Boluda, J.; Colom Palero, RJ. (2013). Level set implementation for the simulation of anisotropic etching: application to complex MEMS micromachining. Journal of Micromechanics and Microengineering. 23(7). https://doi.org/10.1088/0960-1317/23/7/075017S237Weirauch, D. F. (1975). Correlation of the anisotropic etching of single−crystal silicon spheres and wafers. Journal of Applied Physics, 46(4), 1478-1483. doi:10.1063/1.321787Seidel, H. (1990). Anisotropic Etching of Crystalline Silicon in Alkaline Solutions. Journal of The Electrochemical Society, 137(11), 3612. doi:10.1149/1.2086277Zielke, D., & Frühauf, J. (1995). Determination of rates for orientation-dependent etching. Sensors and Actuators A: Physical, 48(2), 151-156. doi:10.1016/0924-4247(95)00993-0Wind, R. A., & Hines, M. A. (2000). Macroscopic etch anisotropies and microscopic reaction mechanisms: a micromachined structure for the rapid assay of etchant anisotropy. Surface Science, 460(1-3), 21-38. doi:10.1016/s0039-6028(00)00479-9Gosálvez, M. A., Sato, K., Foster, A. S., Nieminen, R. M., & Tanaka, H. (2007). An atomistic introduction to anisotropic etching. Journal of Micromechanics and Microengineering, 17(4), S1-S26. doi:10.1088/0960-1317/17/4/s01Sato, K., Shikida, M., Matsushima, Y., Yamashiro, T., Asaumi, K., Iriye, Y., & Yamamoto, M. (1998). Characterization of orientation-dependent etching properties of single-crystal silicon: effects of KOH concentration. Sensors and Actuators A: Physical, 64(1), 87-93. doi:10.1016/s0924-4247(97)01658-0Zubel, I., & Kramkowska, M. (2002). The effect of alcohol additives on etching characteristics in KOH solutions. Sensors and Actuators A: Physical, 101(3), 255-261. doi:10.1016/s0924-4247(02)00265-0Charbonnieras, A. R., & Tellier, C. R. (1999). Characterization of the anisotropic chemical attack of {hk0} silicon plates in a T.M.A.H. solution. Sensors and Actuators A: Physical, 77(2), 81-97. doi:10.1016/s0924-4247(99)00020-5Shikida, M., Sato, K., Tokoro, K., & Uchikawa, D. (2000). Differences in anisotropic etching properties of KOH and TMAH solutions. Sensors and Actuators A: Physical, 80(2), 179-188. doi:10.1016/s0924-4247(99)00264-2Gosálvez, M. A., Zubel, I., & Viinikka, E. (2010). Wet Etching of Silicon. Handbook of Silicon Based MEMS Materials and Technologies, 375-407. doi:10.1016/b978-0-8155-1594-4.00024-3Pal, P., Gosalvez, M. A., & Sato, K. (2010). Silicon Micromachining Based on Surfactant-Added Tetramethyl Ammonium Hydroxide: Etching Mechanism and Advanced Applications. Japanese Journal of Applied Physics, 49(5), 056702. doi:10.1143/jjap.49.056702Zubel, I., & Kramkowska, M. (2004). Etch rates and morphology of silicon (h k l) surfaces etched in KOH and KOH saturated with isopropanol solutions. Sensors and Actuators A: Physical, 115(2-3), 549-556. doi:10.1016/j.sna.2003.11.010Fruhauf, J., Trautmann, K., Wittig, J., & Zielke, D. (1993). A simulation tool for orientation dependent etching. Journal of Micromechanics and Microengineering, 3(3), 113-115. doi:10.1088/0960-1317/3/3/004Than, O., & Büttgenbach, S. (1994). Simulation of anisotropic chemical etching of crystalline silicon using a cellular automata model. Sensors and Actuators A: Physical, 45(1), 85-89. doi:10.1016/0924-4247(94)00820-5Camon, H., Gue, A. M., Danel, J. S., & Djafari-Rouhani, M. (1992). Modelling of anisotropic etching in silicon-based sensor application. Sensors and Actuators A: Physical, 33(1-2), 103-105. doi:10.1016/0924-4247(92)80237-wGosalvez, M. ., Nieminen, R. ., Kilpinen, P., Haimi, E., & Lindroos, V. (2001). Anisotropic wet chemical etching of crystalline silicon: atomistic Monte-Carlo simulations and experiments. Applied Surface Science, 178(1-4), 7-26. doi:10.1016/s0169-4332(01)00233-1Zhenjun Zhu, & Chang Liu. (2000). Micromachining process simulation using a continuous cellular automata method. Journal of Microelectromechanical Systems, 9(2), 252-261. doi:10.1109/84.846706Gosalvez, M. A., Yan Xing, & Sato, K. (2008). Analytical Solution of the Continuous Cellular Automaton for Anisotropic Etching. Journal of Microelectromechanical Systems, 17(2), 410-431. doi:10.1109/jmems.2008.916339Ferrando, N., Gosálvez, M. A., Cerdá, J., Gadea, R., & Sato, K. (2011). Faster and exact implementation of the continuous cellular automaton for anisotropic etching simulations. Journal of Micromechanics and Microengineering, 21(2), 025021. doi:10.1088/0960-1317/21/2/025021Ferrando, N., Gosálvez, M. A., Cerdá, J., Gadea, R., & Sato, K. (2011). Octree-based, GPU implementation of a continuous cellular automaton for the simulation of complex, evolving surfaces. Computer Physics Communications, 182(3), 628-640. doi:10.1016/j.cpc.2010.11.004Moktadir, Z., & Camon, H. (1997). Monte Carlo simulation of anisotropic etching of silicon: investigation of surface properties. Modelling and Simulation in Materials Science and Engineering, 5(5), 481-488. doi:10.1088/0965-0393/5/5/004Flidr, J., Huang, Y.-C., & Hines, M. A. (1999). An atomistic mechanism for the production of two- and three-dimensional etch hillocks on Si(111) surfaces. The Journal of Chemical Physics, 111(15), 6970-6981. doi:10.1063/1.479990Gos lvez, M. A., & Nieminen, R. M. (2003). Surface morphology during anisotropic wet chemical etching of crystalline silicon. New Journal of Physics, 5, 100-100. doi:10.1088/1367-2630/5/1/400Xing, Y., Gosálvez, M. A., Sato, K., Tian, M., & Yi, H. (2012). Evolutionary determination of kinetic Monte Carlo rates for the simulation of evolving surfaces in anisotropic etching of silicon. Journal of Micromechanics and Microengineering, 22(8), 085020. doi:10.1088/0960-1317/22/8/085020Xing, Y., Gosálvez, M. A., Sato, K., & Yi, H. (2009). Orientation-dependent surface morphology of crystalline silicon during anisotropic etching using a continuous cellular automaton. Journal of Micromechanics and Microengineering, 20(1), 015019. doi:10.1088/0960-1317/20/1/015019Zhou, Z., Huang, Q., Li, W., & Deng, W. (2007). A cellular automaton-based simulator for silicon anisotropic etching processes considering high index planes. Journal of Micromechanics and Microengineering, 17(4), S38-S49. doi:10.1088/0960-1317/17/4/s03Gosálvez, M. A., Xing, Y., Sato, K., & Nieminen, R. M. (2009). Discrete and continuous cellular automata for the simulation of propagating surfaces. Sensors and Actuators A: Physical, 155(1), 98-112. doi:10.1016/j.sna.2009.08.012Ferrando, N., Gosálvez, M. A., & Colóm, R. J. (2012). Evolutionary continuous cellular automaton for the simulation of wet etching of quartz. Journal of Micromechanics and Microengineering, 22(2), 025021. doi:10.1088/0960-1317/22/2/025021Osher, S., & Sethian, J. A. (1988). Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 79(1), 12-49. doi:10.1016/0021-9991(88)90002-2Adalsteinsson, D., & Sethian, J. A. (1995). A Level Set Approach to a Unified Model for Etching, Deposition, and Lithography I: Algorithms and Two-Dimensional Simulations. Journal of Computational Physics, 120(1), 128-144. doi:10.1006/jcph.1995.1153Adalsteinsson, D., & Sethian, J. A. (1995). A Level Set Approach to a Unified Model for Etching, Deposition, and Lithography II: Three-Dimensional Simulations. Journal of Computational Physics, 122(2), 348-366. doi:10.1006/jcph.1995.1221Adalsteinsson, D., & Sethian, J. A. (1997). A Level Set Approach to a Unified Model for Etching, Deposition, and Lithography. Journal of Computational Physics, 138(1), 193-223. doi:10.1006/jcph.1997.5817Ertl, O., & Selberherr, S. (2009). A fast level set framework for large three-dimensional topography simulations. Computer Physics Communications, 180(8), 1242-1250. doi:10.1016/j.cpc.2009.02.002Ertl, O., & Selberherr, S. (2010). Three-dimensional level set based Bosch process simulations using ray tracing for flux calculation. Microelectronic Engineering, 87(1), 20-29. doi:10.1016/j.mee.2009.05.011Burzynski, T., & Papini, M. (2010). Level set methods for the modelling of surface evolution in the abrasive jet micromachining of features used in MEMS and microfluidic devices. Journal of Micromechanics and Microengineering, 20(8), 085004. doi:10.1088/0960-1317/20/8/085004Radjenović, B., Lee, J. K., & Radmilović-Radjenović, M. (2006). Sparse field level set method for non-convex Hamiltonians in 3D plasma etching profile simulations. Computer Physics Communications, 174(2), 127-132. doi:10.1016/j.cpc.2005.09.010Radjenović, B., Radmilović-Radjenović, M., & Mitrić, M. (2006). Nonconvex Hamiltonians in three dimensional level set simulations of the wet etching of silicon. Applied Physics Letters, 89(21), 213102. doi:10.1063/1.2388860Branislav, R., & Marija, R.-R. (2010). Level set simulations of the anisotropic wet etching process for device fabrication in nanotechnologies. Hemijska industrija, 64(2), 93-97. doi:10.2298/hemind100205008rRadjenović, B., Radmilović-Radjenović, M., & Mitrić, M. (2010). Level Set Approach to Anisotropic Wet Etching of Silicon. Sensors, 10(5), 4950-4967. doi:10.3390/s100504950Radjenović, B., & Radmilović-Radjenović, M. (2011). Three-Dimensional Simulations of the Anisotropic Etching Profile Evolution for Producing Nanoscale Devices. Acta Physica Polonica A, 119(3), 447-450. doi:10.12693/aphyspola.119.447Crandall, M. G., & Lions, P.-L. (1984). Two approximations of solutions of Hamilton-Jacobi equations. Mathematics of Computation, 43(167), 1-1. doi:10.1090/s0025-5718-1984-0744921-8Whitaker, R. T. (1998). International Journal of Computer Vision, 29(3), 203-231. doi:10.1023/a:1008036829907Gomes, J., & Faugeras, O. (2000). Reconciling Distance Functions and Level Sets. Journal of Visual Communication and Image Representation, 11(2), 209-223. doi:10.1006/jvci.1999.0439Fukuzawa, K., Terada, S., Shikida, M., Amakawa, H., Zhang, H., & Mitsuya, Y. (2007). Mechanical design and force calibration of dual-axis micromechanical probe for friction force microscopy. Journal of Applied Physics, 101(3), 034308. doi:10.1063/1.2434825Schröpfer, G., Labachelerie, M. de, Ballandras, S., & Blind, P. (1998). Collective wet etching of a 3D monolithic silicon seismic mass system. Journal of Micromechanics and Microengineering, 8(2), 77-79. doi:10.1088/0960-1317/8/2/008Wilke, N., Reed, M. L., & Morrissey, A. (2006). The evolution from convex corner undercut towards microneedle formation: theory and experimental verification. Journal of Micromechanics and Microengineering, 16(4), 808-814. doi:10.1088/0960-1317/16/4/018Liang, J., Kohsaka, F., Matsuo, T., & Ueda, T. (2007). Wet Etched High Aspect Ratio Microstructures on Quartz for MEMS Applications. IEEJ Transactions on Sensors and Micromachines, 127(7), 337-342. doi:10.1541/ieejsmas.127.337Hida, H., Shikida, M., Fukuzawa, K., Murakami, S., Sato, K., Asaumi, K., … Sato, K. (2008). Fabrication of a quartz tuning-fork probe with a sharp tip for AFM systems. Sensors and Actuators A: Physical, 148(1), 311-318. doi:10.1016/j.sna.2008.08.02

Estudio, Modelado e Implementación Paralela de Sistemas Celulares Utilizados en Microfabricación

La presente tesis toma como eje central el modelado de sistemas dinámicos mediante Autómatas Celulares (ACs). Los ACs permiten modelar un sistema enunciando el comportamiento microscópico a fin de obtener un comportamiento macroscópico correcto. Una de los principales campos donde esta metodología ha sido aplicada (y la cual forma otro de los puntos centrales de esta tesis) es el modelado del Grabado Anisótropo Húmedo (GAH). El GAH es un proceso químico el cual permite realizar microestructuras de silicio tridimensionales, lo que le ha permitido convertirse en una importante técnica de microfabricación. El GAH se utiliza para el micromaquinado de Sistemas Micro-Electro-Mecánicos (MEMS). Los MEMS consisten en la integración de elementos mecánicos, sensores, actuadores y electrónica en un substrato de silicio común a través de la tecnología de microfabricación. Los MEMS tienen una gran influencia en la industria puesto que dispositivos fabricados mediante esta tecnología se utilizan de forma intensiva en diversos campos tales como: sistemas de seguridad en automoción, sensores de movimiento en electrónica de consumo o inyectores en sistemas de impresión. El GAH es un proceso complejo cuyo resultado depende en gran medida de los diversos parámetros del proceso: (disolución, temperatura, tiempo), por lo que la utilización de un simulador previo a la realización del experimento puede suponer un gran ahorro en cuestión de tiempo y material. Los simuladores actuales de GAH basados en ACs poseen diversas limitaciones: Tiempos de computación muy elevados debido a los altos requisitos computacionales de los ACs, un reducido conjunto de calibraciones existentes, así como la imposibilidad de simular el GAH basado en nuevos atacantes tales como TMAH+Triton. La resolución de estas limitaciones es abordada en diversos capítulos de la tesis.Ferrando Jódar, N. (2011). Estudio, Modelado e Implementación Paralela de Sistemas Celulares Utilizados en Microfabricación [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/10984Palanci

Genetic programming and cellular automata for fast flood modelling on multi-core CPU and many-core GPU computers

Many complex systems in nature are governed by simple local interactions, although a number are also described by global interactions. For example, within the field of hydraulics the Navier-Stokes equations describe free-surface water flow, through means of the global preservation of water volume, momentum and energy. However, solving such partial differential equations (PDEs) is computationally expensive when applied to large 2D flow problems. An alternative which reduces the computational complexity, is to use a local derivative to approximate the PDEs, such as finite difference methods, or Cellular Automata (CA). The high speed processing of such simulations is important to modern scientific investigation especially within urban flood modelling, as urban expansion continues to increase the number of impervious areas that need to be modelled. Large numbers of model runs or large spatial or temporal resolution simulations are required in order to investigate, for example, climate change, early warning systems, and sewer design optimisation. The recent introduction of the Graphics Processor Unit (GPU) as a general purpose computing device (General Purpose Graphical Processor Unit, GPGPU) allows this hardware to be used for the accelerated processing of such locally driven simulations. A novel CA transformation for use with GPUs is proposed here to make maximum use of the GPU hardware. CA models are defined by the local state transition rules, which are used in every cell in parallel, and provide an excellent platform for a comparative study of possible alternative state transition rules. Writing local state transition rules for CA systems is a difficult task for humans due to the number and complexity of possible interactions, and is known as the ‘inverse problem’ for CA. Therefore, the use of Genetic Programming (GP) algorithms for the automatic development of state transition rules from example data is also investigated in this thesis. GP is investigated as it is capable of searching the intractably large areas of possible state transition rules, and producing near optimal solutions. However, such population-based optimisation algorithms are limited by the cost of many repeated evaluations of the fitness function, which in this case requires the comparison of a CA simulation to given target data. Therefore, the use of GPGPU hardware for the accelerated learning of local rules is also developed. Speed-up factors of up to 50 times over serial Central Processing Unit (CPU) processing are achieved on simple CA, up to 5-10 times speedup over the fully parallel CPU for the learning of urban flood modelling rules. Furthermore, it is shown GP can generate rules which perform competitively when compared with human formulated rules. This is achieved with generalisation to unseen terrains using similar input conditions and different spatial/temporal resolutions in this important application domain