I have a 2nd order ODE that is obtained for a laminated composite with surface bonded PZT sensor and actuator. Currently I am using Newmark's time integration for the solution, but the computation time is high. The mass, damping and stiffness matrices are band diagonal. Can someone suggest a numerical solution strategy to save computational time by taking advantage of the sparsity in the M, C and K matrices?
I suggest the following two options:
1.) An explicit scheme.
2.) An implicit scheme other than the Newmark method. Newmark method does not have enough high-frequency damping; this forces you to use smaller time steps to get stable solution(s).
For further details, go through my blog and my paper
https://ckadapa.wordpress.com/2017/06/23/newmark-beta-method-disadvantages/
Article On the advantages of using the first-order generalised-alpha...
There are several published sparse matrices algorithms for solving systems of equations handly only non-zero elements dependently on the discretization of your ordinary differential equations see ACM Digital Library on http://dl.acm.org
What type of software are u using? If u use matlab (kind of slow for this kind of computations) u could try to use sparse matrices and perform matrix inversions with a numerical method like pcg (preconditioned conjugate gradient) u could alternatively try to manually break down the computations in pcg if your matrices have a well defined sparsity pattern and exexute them in parallel
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