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We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities.
It was demonstrated in earlier work that a nondefective, linear dynamical system with an invertible mass matrix in free or forced motion may be decoupled in the configuration space by a real and isospectral transformation.
We extend this work by developing a procedure for decoupling a linear dynamical system with a singular mass matrix in the configuration space, transforming the original differential-algebraic system into decoupled sets of real, independent, first- and second-order differential equations.
Lumped massmatrix is preferred, if not mandatory, over consistent mass matrix in thecase of explicit time integration.
The Block Lanczos method uses an assembled stiffness and mass matrix in addition to factoring matrices that are a combination of the mass and stiffness matrices computed at various shift points (ANSYS 2012).
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We will then analyse the corresponding stiffness and mass matrices in terms of sparsity patterns and conditioning numbers.
The principle of virtual displacements in conjunction with the finite element method (FEM) is used to formulate stiffness and mass matrices in terms of fundamental nuclei.
The model is used to express the calculations of the reduced stiffness and mass matrices in a declarative query language and thereby letting the database decide how to execute the operations and manage the memory.
The method extends Jie Shen's algorithm for 2D problems by using the diagonalization of the three mass matrices in the three spatial directions and fully exploits the direct product nature of the spectral approximation.
We present a Mathematica package designed to automatize the expansion of transition amplitudes calculated in the mass eigenstates basis (i.e. expressed in terms of physical masses and mixing matrices) into series of "mass insertions", defined as off-diagonal entries of mass matrices in Lagrangian before diagonalization and identification of the physical states.
A double diagonalization process is employed pivoting around the eigenstructure of the pentadiagonal mass matrices in both directions, instead of the full stiffness matrices encountered in the classical variational formulation of the problem with a weak natural imposition of the derivative boundary condition.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com