We present an efficient numericalNumerical method for time-harmonic acoustics problemsProblem, consisting of a discrete exterior calculus (DEC) discretizationDiscretization of the time-dependent wave equationEquation and a controllability-based optimizationOptimization procedure. ForControlledTimeIntegrationTime improved performance in the harmonic problemProblem domainDomain, the method is modified with an exact timestepping scheme and a Hodge star operator optimized for harmonic waves. The presented method’s effectiveness is investigated experimentally by solving a scattering problemProblem with varying degrees of geometric complexity. The controllability method shows most benefits in highly nonconvex geometries, where a simple asymptotic iteration does not reliably converge to a solutionSolution. The harmonic Hodge star operator is found to increase accuracyAccuracy significantly without imposing a runtime performance cost. Quality of the computation meshMesh is identified as a key issue affecting the method’s accuracyAccuracy and reliability.