Abstract
Recently, multisymplectic discretizations have been drawing much attention and, therefore, have become the vigorous component of the structure-preserving algorithms. In this chapter, we systematically develop what our research group has achieved in the field of multisymplectic discretizations. Some very interesting new issues arising in this field are also given. Multisymplectic and variational integrators are studied from a comparative point of view. The implementation issues of multisymplectic integrators are discussed, and composition methods to construct higher order multisymplectic integrators are presented. The equivalence of variational integrators to multisymplectic integrators is proved. Several generalizations are also described.
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