An explicit second order spectral element method for acoustic waves |
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Authors: | Elena Zampieri Luca F Pavarino |
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Institution: | (1) Department of Mathematics, Università di Milano, Via Saldini 50, 20133 Milano, Italy |
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Abstract: | The acoustic wave equation is here discretized by conforming spectral elements in space and by the second order leap-frog
method in time. For simplicity, homogeneous boundary conditions are considered. A stability analysis of the resulting method
is presented, providing an upper bound for the allowed time step that is proportional to the size of the elements and inversely
proportional to the square of their polynomial degree. A convergence analysis is also presented, showing that the convergence
error decreases when the time step or the size of the elements decrease or when the polynomial degree increases. Several numerical
results illustrating these results are presented.
Mathematics subject classifications (2000) 65M06, 65M70, 65M12
This work was supported by MIUR (PRIN 2001 “Metodi numerici avanzati per equazioni alle derivate parziali di interesse applicativo”). |
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Keywords: | acoustic waves spectral elements explicit time advancing schemes stability |
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