  Nowadays integration of mass matrix components in the element domain is
performed using various numerical integration schemes, each one possess
different level of accuracy, alters in number of integration (Gauss) points and
requires different amount of computations. Herein semi-analytical approach is
suggested. Metric (Jacobian determinant) is approximately modeled using its
evaluations in certain points. Analytical integration is performed to derive
simple explicit closed-form expressions for each term of the mass matrix. Two
schemes are discussed: the first assumes constant metric (CM) in the initial
domain, using evaluation at the centroid. The second allows for linear
variation of the metric (LM linear metric) in the domain using 3 additional
evaluation points. Both schemes are exact for rectangular and non-rectangular
parallelepiped mesh. Careful symbolic manipulations and convenient choice of
evaluation points allow us to avoid unnecessary operations. The accuracy of
both schemes is studied numerically using randomly generated coarse mesh.
Significant superiority in accuracy over equivalent schemes is reported. An
important implication of this study is that it can replace currently used
schemes.
