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This paper reports on an efficient finite-element scheme for computer-aided design of a clinical magnetic resonance imaging (MRI) scanner. The modeling scheme allows the full three-dimensional calculation of the electromagnetic, mechanical, and acoustic fields, including their mutual couplings. The validity of the computer simulations has been verified by appropriate measurements. Applications include the optimization of the gradient coil and the superconducting magnet with respect to eddy-current losses in the cryostat and the emitted noise.