Ontology similarity calculation and ontology mapping are crucial research topics in information retrieval. Ontology, as a concept structure model, is widely used in biology, physics, geography and social sciences. In this paper, we present new algorithms for ontology similarity measurement and ontology mapping using harmonic analysis and diffusion regularization on hypergraph. The optimal function gets from new algorithms manifests good smoothness and well reflects the structure of the ontology graph. Two experimental results show that the proposed new technologies have high accuracy and efficiency on ontology similarity calculation and ontology mapping in certain applications.