FUNDAMENTAL PROBLEMS IN FINITE ELEMENT SIMULATION OF WAVE MOTION

The transmitting boundary condition is written in a compact form, which can be direct-ly incorporated into finite elements. Basic characteristics of discretization are analyzed throughstudies on wave motion in a one-dimensional discrete model and their differences from those in thecorresponding continuum. Tbe analysis leads to identifying a frequency band within which thesimulation is possible, and to a suggestion of using the lumped-mass finite element model forthe simulation. Mechanism of the oscillation instability is then illuminated in the frequencydomain by amplification at the artificial boundary and multi-reflection of wave motion in afinite discrete model. Based on understanding of the mechanism, a modified transmittingboundary condition is devised for eliminating the instability. The special stability criterion forthe modified boundary is finally presented for the one-dimensional model.

FUNDAMENTAL PROBLEMS IN FINITE ELEMENT SIMULATION OF WAVE MOTION

The transmitting boundary condition is written in a compact form, which can be direct- ly incorporated into finite elements. Basic characteristics of discretization are analyzed through studies on wave motion in a one-dimensional discrete model and their differences from those in the corresponding continuum. Tbe analysis leads to identifying a frequency band within which the simulation is possible, and to a suggestion of using the lumped-mass finite element model for the simulation. Mechanism of the oscillation instability is then illuminated in the frequency domain by amplification at the artificial boundary and multi-reflection of wave motion in a finite discrete model. Based on understanding of the mechanism, a modified transmitting boundary condition is devised for eliminating the instability. The special stability criterion for the modified boundary is finally presented for the one-dimensional model.