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COMSOL Multiphysics™

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assemble<br />

matrix contribution (from one element) is A l<br />

= { A l,<br />

ij<br />

} and the currently<br />

assembled global matrix is A = { A ij<br />

} then the entry A ij<br />

is replaced by a zero if<br />

A ij<br />

+ [ A l<br />

] ij<br />

< ε a<br />

max kl<br />

A l,<br />

kl<br />

where [ ] ij<br />

denotes the contribution from a local matrix to the global matrix entry<br />

ij, and where ε a<br />

is the assembly tolerance controlled by the property Assemtol. For<br />

certain types of shape functions the procedure described above is not always safe to<br />

perform. This is the case for shape function elements with degrees of freedoms that<br />

are of different types, for example when a field variable and its spatial derivative is<br />

combined (as in the shherm or sharg_2_5 elements), or when the displacement and<br />

displacement angles are combined (as in some Euler Beam elements in the<br />

Structural Mechanics Module). For this reason, the above process is never used for<br />

local matrix contributions from these types of shape function elements. If the<br />

Assemtol is zero then no elements are neglected, but the removal of zeros are still<br />

performed. If Assemtol is negative, no elements are neglected, and zeros are not<br />

removed from the assembled matrices.<br />

The property Blocksize determines the number of mesh elements that are<br />

assembled together in a vectorized manner. A low value gives a lower memory<br />

consumption, while a high value might give a better performance.<br />

The properties Complexfun and Matherr are described in femsolver.<br />

The property Const gives a list of definitions of constants to be used in evaluations.<br />

This list is a row cell array with alternating constant names and numeric values. This<br />

list is appended to the list given in fem.const. If there is a conflict, the definition<br />

in Const is used.<br />

The properties Eigname and Eigref are described in femeig.<br />

The property Out determines which matrices to output. Ksp is the sparsity pattern<br />

of K. The matrices A, AL, BE, C, and Q are the contributions to the K matrix that<br />

come from the coefficients a, α, β, c, and q, respectively. The vectors F, G, and GA<br />

are the contributions to the L vector that come from the terms f (or F), g (or G),<br />

and γ (or Γ), respectively. The matrix H is the contribution to the N matrix that<br />

comes from the h coefficient. The vector R is the contribution to the M vector that<br />

comes from the r (or R) coefficient. The matrix DA is the contribution to the D<br />

matrix that comes from the d a coefficient. The matrix EA is the contribution to the<br />

E matrix that comes from the e a coefficient.<br />

31

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