Actas JP2011 - Universidad de La Laguna

Actas XXII Jornadas de Paralelismo (JP2011) , La Laguna, Tenerife, 7-9 septiembre 201130. Equation system Ax=B has 3408 equations. Resolutionprocess needs 6 iterations due to the thermalpart of the problem.4. Proof Case 4: It consists of two solids in contact.Both of them are prisms; solid A is made upby 384 elements and solid B is made up by 752 elements.The number of elements that belong to thecontact zone is 128 for both solids. The type of contactbetween solids is imperfect and the referencetemperature is 30. Equation system Ax=B has 3408equations. Resolution process requires 2 iterationsdue to the thermal part of the problem.Fig. 4. This figure shows the execution time comparison of thethermal problem explained. As it is showed, the executiontime in Fortran’s version is bigger than in Java’s version,so, in this case, we have managed a meaningful reductionin execution time.Fig. 3. This figure shows solids from Proof Case 3 as they arerepresented on the BEMAPEC’s application graphical environment.Points are the nodes of each element obtainedafter meshing. The white plane means XZ symmetry andthe grey plane corresponds to YZ symmetry.D. Executed time comparisonPrevious mentioned problems for FORTRAN’s applicationversion and BEMAPEC application aboutexecuted time are displayed as it is shown on thegraphics 4, 5 and 6. When we solved the thermalproblem using JAVA’s application version, we managean improvement because the execution time isreduced. If we analyze results obtained in elasticproblems, we could draw as conclusion that higherthe number of equations which made up the equationsystem is, more significant the reduction in executiontime is. In contrast, when the equation systemis lesser, Java’s application version increase a bit theexecution time, although the difference is not veryimportant.Finally, thermoelastic problems’ behaviour is different.In these problems, it is less important thenumber of equations than the number of iterations.For example, in cases 3 and 4, the number of equationsis the same, but in case 3 there are 4 iterationsmore than in case 2 and we obtained better timeswhen the number of iterations is higher. When thenumber of iterations is less, the execution time ispractically the same.As it is can be observed, the more elements makeup solids, the higher is the difference between times,and therefore, the amount of equations is higher. Inthose cases, Java’s application version is more efficiently.V. Conclusions and Future WorksIn this work, we have used OOP techniques tosolve contact problems between 3D solids. So that,after coefficients have been calculated using the previousversion of BEMAPEC, assembly matrixes ofequation system Ax=B is done. After that, GaussFig. 5. This figure shows the execution time comparison ofelastic problems which have been proved. We managed agreat reduction in cases 1, 4 and 5. However, slightly weget worse the execution time in case 2 and 3. This is dueto our application is more effective when the number ofequations in the equation system is large.Method with pivot is used to solve it because, actually,this is the most efficiently method on resolvingequation systems when the number of them is higher.Then, problem is solved using methods that dependon the type of problem (thermal, elastic o thermoelastic).Process finishes with the writing of obtainedresults into an output file.When equation number that makes up systemequation is large, the execution time for the resolutionproblem is lower in Java’s version than FOR-TRAN’s one. In contrast, when equation system hasfewer equations, the FORTRAN’s version is more efficient.However, in this kind of problems is usual tohave a large number of equations.Further works include to parallelize the resolutionprocess in order to reduce the execution time as wellas using different techniques to solve the equationsystem.VI. AcknowledgementsThis work has been partially supported by the researchgrants program from the University of León(Spain).Referencias[1] Matti Stenroos, Helsinki bem library., [Online]. Available:http://peili.hut.fi/BEM.JP2011-151