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FEM (Finite Elements Method)

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FEM (Finite Elements Method)

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  1. LIGHTWEIGHT STRUCTURES in CIVIL ENGINEERINGINTERNATIONAL SEMINAR of IASS POLISH CHAPTEROrganized by Polish Chapter ofInternational Association for Shell and Spatial StructuresWarsaw-Częstochowa, 3 December, 2004OVERLOADING OF OPERATORS IN FEMA SYSTEMW. PRZYBYŁO 1 and M. MAŹNIEWSKI 21Professor, Częstochowa University of Technology, ul. Akademicka 3, 42-200 Częstochowa, POLAND2PhD. student, Częstochowa University of Technology, ul. Akademicka 3, 42-200 Częstochowa, POLAND

  2. FEM (Finite Elements Method) • Constructions are divided into many elements • Elements are described with matrices • Hypermatrix - matrix of matrices • Problems associated with matrices: • high requirements of disk and memory space • high requirements of computational power • costly and time-consuming calculations

  3. Characteristics of matrix operations • Problems' solutions are constructed as a set of subtasks • Subtasks are executed one by another • Some subtasks are repeated many times with different data-sets • Some subtasks are independent one of another • Subtasks can be executed simultaneously

  4. Parallelization of multiplying matrices

  5. Comparison of computer systems • Single computer – one CPU • Symetric Multiprocessor(SMP) • Parallel computer • many processors in one box • one processor – one task • Clusters – set of computers jointed with network • Saving money by using owned hardware • Big computational power with low cost • Easy enlarging • Reliable calculations • Fail-safe system

  6. Speeding-up calculations • Simultaneous subtasks' execution • Computer programs' parallelization • Building clustered systems • Requirements: • Synchronization of data • Interprocess communication • Network communication

  7. Modelling algorithms into computer programs • Algorithm – description of problem solution • Algorithms are constructed with cooperation of specialists • Computer program – representation of algorithm • different syntax of programming languages • Only programmers understand source code • Mathematic operations replaced with programming operations

  8. Overloading of operators • Arithmetic operators – works only with basic data-types(char, integer value, real value...) • Defining own data-types – Objective Programming • Matrix operations • Definition of object: MATRIX • Overloading operators – allowing them work with user-defined data-types • Problems with matrices operations • Large matrices need large disk and memory spaces • Assignment of matrices – copying one matrix to another

  9. Overloading of operators cont. • Classic mode • a:=1, b:= 2 – integer values • c := a + b, c = 3 – integer value • Overloading operators • A – matrix, dimension: n x n • B – matrix, dimension: n x n • C : = A + B - matrix, dimension n x n • D : = A * B – matrix, dimension n x n

  10. FEMA System • Designed for matrices and hypermatrices operations • Modular system for modular operations(parallelization enabled) • Maximum dimension of data sets, minimum time of processing

  11. Proposed approach • Overloading matrix operations • Replacing copying of matrices – with commands from FEMA system • Dividing task into subtasks • Writing steering files for every subtask • Sending steering files to nodes of clusters • Processing calculations in professional system(FEMA) • Aggregation of calculations' results

  12. Example • Adding matrices: • in source code: C = A + B • in result : PHAH A B C • Multiplying matrices: • in source code: C = A * B • in result : PHMH A B C

  13. Appendix: Parallel example • Steering file is read by master-program • Worker-program is invoked • Master-program sends steering file to worker • Worker-program writes steering file to hard-disk • Worker-program invokes FEMA system • FEMA system read task-definition and input data • FEMA system executes operations and writes results to hard-disk

  14. Steering file example (fema.CIN) • DDEX • DEX-BAT • DDEX7 • 2 • 3 • Y • Y • N • N • END • END

  15. Console output • [1:t40005] Master process..262149..[ bind and ready to distribute tasks ].. • [1:t40005] Master [262149]..Checking steering-file [/tmp/fema.CIN] structure...OK • [1:t40005] Worker-process..ID...262150: [ ready to execute tasks ] • [1:t40005] Process: [262149] ready to send steering file.. • [1:t40006] Process: [262150] ready to get steering file.. • [1:t40005] [262149]..We've read: • [1:t40005] DDEX • [1:t40005] DEX-BAT • [1:t40005] DDEX7 • [1:t40005] 2 • [1:t40005] 3 • [1:t40005] Y • [1:t40005] Y • [1:t40005] N • [1:t40005] N • [1:t40005] END • [1:t40005] END • [1:t40005] END • [1:t40005] Process [262149]..sending steering file to worker(s).. • [1:t40006] Process: [262150] retrieved cmd: • [1:t40006] ..DDEX • [1:t40006] DEX-BAT • [1:t40006] DDEX7 • [1:t40006] 2 • [1:t40006] 3 • [1:t40006] Y • [1:t40006] Y • [1:t40006] N • [1:t40006] N

  16. [1:t40006] END • [1:t40006] END • [1:t40006] END • [1:t40005] Process: [262149] - retrieved confirmation.. • [1:t40005] Process: [262149] exiting.. • [1:t40005] EOF • [1:t40006] ....confirmation sent to master.. • [1:t40006] Process: [262150]..Attempting to write steering file [/home/pvm3/bin/LINUX/FEMA/task/fema.CIN].. • [1:t40006] Process: [262150] - [ OK ] file has been written • [1:t40006] Process: [262150]..Attempting to run FEMA system.. • [1:t40006] Process: [262150]..checking for task-definition file.. • [1:t40006] Process: [262150] - [ OK ] task-definition file is proper.. • [1:t40006] Process: [262150]..running FEMA system.. • [1:t40006] sh: CLS: command not found • [1:t40006] sh: PAUSE: command not found • [1:t40006] sh: CLS: command not found • [1:t40006] sh: CLS: command not found • [1:t40006] sh: CLS: command not found • [1:t40006] [34;1m******************************************************************************** • [1:t40006] WELCOME TO FEMA DATABASE MADE BY FEMA ENGINEERING LTD • [1:t40006] YOU HAVE SELECTED /home/pvm3/bin/LINUX/f88.exe, • [1:t40006] WITH /home/pvm3/bin/LINUX/FEMA/task/fema.INP AS ARGUMENT • [1:t40006] ******************************************************************************** • [1:t40006] [0m**************************************************************************** • [1:t40006] EOF

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