FINITE ELEMENT SOLUTION OF WAVE EQUATION WITH REDUCTION OF THE VELOCITY DISPERSION AND SPURIOUS REFLECTION

Abstract

THE OBJECTIVE OF THIS PAPER IS TO PRESENT A FINITE ELEMENT SOLUTION FOR THE WAVE PROPAGATION PROBLEMS WITH A REDUCTION OF THE VELOCITY DISPERSION AND SPURIOUS REFLECTION. TO THIS END, A HIGH-ORDER TWO-STEP DIRECT INTEGRATION ALGORITHM FOR THE WAVE EQUATION IS ADOPTED. THE SUGGESTED ALGORITHM IS FORMULATED IN TERMS OF TWO HERMITIAN FINITE DIFFERENCE OPERATORS WITH A SIXTH-ORDER LOCAL TRUNCATION ERROR IN TIME. THE TWO-NODE LINEAR FINITE ELEMENT PRESENTING THE FOURTH-ORDER OF LOCAL TRUNCATION ERROR IS CONSIDERED. THE NUMERICAL RESULTS REVEAL THAT ALTHOUGH THE ALGORITHM COMPETES WITH HIGHER-ORDER ALGORITHMS PRESENTED IN THE LITERATURE, THE COMPUTATIONAL EFFORT REQUIRED IS SIMILAR TO THE EFFORT REQUIRED BY THE AVERAGE ACCELERATION NEWMARK METHOD. MORE THAN THAT, THE INTEGRATION WITH THE LUMPED MASS MODEL SHOWS SIMILAR RESULTS TO THE INTEGRATION USING THE AVERAGE ACCELERATION NEWMARK FOR THE CONSISTENT MASS MODEL, WHICH INVOLVES A HIGHER NUMBER OF COMPUTATIONAL OPERATIONS.