Dynamical reduced basis methods for Hamiltonian systems
نویسندگان
چکیده
Abstract We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development reduced basis methods for such models is challenged by two main factors: the rich geometric structure encoding physical stability properties dynamics its local low-rank nature. To address these aspects, we propose a nonlinear structure-preserving where phase space evolves in time. In spirit dynamical approximation, obtained symplectic projection vector field onto tangent approximation manifold at each state. A priori error estimates are established terms full solution manifold. For temporal discretization employ splitting techniques. satisfies an evolution equation on orthogonal rectangular matrices having one dimension equal to size model. recast problem matrix develop intrinsic integrators based Lie group techniques together with explicit Runge–Kutta (RK) schemes. resulting shown converge RK integrator their computational complexity depends only linearly model, provided evaluation flow velocity has comparable cost.
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ژورنال
عنوان ژورنال: Numerische Mathematik
سال: 2021
ISSN: ['0945-3245', '0029-599X']
DOI: https://doi.org/10.1007/s00211-021-01211-w