A circuit theoretical method for efficient finite element analysis of acoustical problems

In the last decade, there has been an outstanding improvement in the computer aided design tools for VLSI circuits regarding solution times and the circuit complexity. This study proposes formulating the acoustic field analysis problem using FEM, and employing the recent speed-up techniques used in the circuit simulators. In this work, total mass, stiffness and damping matrices are obtained using the FE approach, and piped into a computer program which generates an equivalent SPICE compatible circuit netlist. This approach makes it possible to use the most recent circuit simulation techniques to simulate the acoustical problems. The equivalent electrical circuit is a resistor-inductor-capacitor (RLC) circuit containing controlled sources to handle the couplings. The circuit matrices are 6 times larger but are sparser. We analyze these circuits with a general-purpose circuit simulation program, HSPICE, which provides high accuracy solutions in a short time. We also use an in-house developed circuit simulation program, MAWE, which makes use of asymptotic waveform evaluation (AWE) technique that has been successfully used in circuit simulation for solutions of large sets of equations. The results obtained on several problems, which are solved in time and frequency domains using circuit simulators and the FE analysis program ANSYS, match each other pretty well. Using circuit simulators instead of conventional method improves simulation speed without a significant loss of accuracy.