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Ultrasound is the collective name of all soundwaves above the range of human

hearing, i.e. above 20 kHz. Such waves were in the thirties the foundation

of the invention of SONAR, which operates at frequencies from 20kHz to

100kHz. The variety of applications for ultrasound increased signicantly

with the discovery of piezoelectric ceramics[2], allowing for frequencies in the

range of MHz. These high frequencies gave rise to non-intrusive analysis

of solid material, such as in welding seams. It was soon realized that the

non-intrusive nature of ultrasound would make it an exellent tool in medical

diagnostic, and successful studies of the human body was conducted in the

U.S.[27], Japan[24] and Sweden[7] in the late forties and early fthies.

The development of ultrasound in medicine over the last sixty years has

been phenomenal, giving rise to, for example, real time three-dimentional

ultrasound[21]. A large part of this development was made possible by the

advances in computer technology, allowing for processing of vast amounts of

data in a short period of time. However, the development of new ultrasonic

transducers is also of great importance, as the signal processing is ultimately

limited by the quality of the input data. The method of designing new

transducer has tradisionally been based on trial and error, supplemented by

one-dimentional simulations. This can however be very expensive and timecomsuming,

as several transducers may have to be constructed in order to

optimize a design. A computer simulation of complete transducer designs

is therefore desired, and for this is the nite element method a very good


The basis of the nite element method was developed seperately by

mathematicians, physicists and engineers, as a way of decomposing complex

problems into simple well known parts. The initial use of the method in

engineering was to replace plates with simple struts[9], but it has later developed

into covering a wide variety


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