Exponential structure-preserving approach for constrained conservative or dissipative systems

We propose a novel symmetric exponential integrator that preserves original energy conservation/dissipation law while holding the global constraints for constrained conservative/dissipative gradient systems. This structure-preserving method is “essentially” explicit and efficient, as it requires only solving an algebraic nonlinear system rather than a nonlinear system with respect to grid functions. The effectiveness and accuracy of our approach are tested by solving several conservative and dissipative partial differential equations. Numerical results confirm the structure-preserving properties and demonstrate excellent performance of the proposed method.