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The present formulation allows the mass matrix to be inverted indirectly.
The results are compared with the updated mass matrix to consider the orthogonality requirement only and the updated stiffness matrix to consider the eigenvalue function only, respectively.
This paper reports an improved finite element method (FEM) for solving acoustic problems by re-distributing the mass in the mass matrix to "tune" the balance, aiming to minimize the dispersion errors.
In contrast to the intrinsic limitations of the proper orthogonal decomposition (POD) analysis, which requires the knowledge of system's mass matrix to extract normal modes and cannot uniquely identify modal subspaces that have similar proper orthogonal values, the SOD is shown to overcome both of these deficiencies.
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The expanded damping matrix is intended to be combined with analytically formulated stiffness and mass matrices to build an experimental analytical hybrid model.
The high- and low-order schemes used are the ones proposed by Lohner who adds diffusion to the high-order scheme by subtracting the lumped-mass matrix from the consistent-mass matrix to give the low-order scheme; the diffusion coefficient is adjusted globally.
Then only minor changes are made to the mass matrix at each iteration, which significantly saves the computation cost.
Since the mass matrix corresponding to the vector valued variables is diagonal, these unknowns can be eliminated exactly.
An alternative square factorization of the mass matrix leads to a closed form expression for its inverse.
A refinement of FLIP [Brackbill and Ruppel, J. Comput. Phys.65, 314 (1986)] is described which uses a mass matrix formulation to achieve greater accuracy and less numerical diffusion over the previous version.
The technique retains all the inertia terms associated with the removed degrees of freedom in an iterated form, which generates the reduced mass matrix similar to that obtained in the Guyan reduction method with a frequency-dependent perturbed term.
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CEO of Professional Science Editing for Scientists @ prosciediting.com