Analysis of GPR Wave Propagation Using CUDA-Implemented Conformal Symplectic Partitioned Runge-Kutta Method
نویسندگان
چکیده
منابع مشابه
University of Cambridge Numerical Analysis Reports Practical Symplectic Partitioned Runge{kutta and Runge{kutta{nystrr Om Methods Practical Symplectic Partitioned Runge{kutta and Runge{kutta{nystrr Om Methods
We present new symmetric fourth and sixth-order symplectic Partitioned Runge{ Kutta and Runge{Kutta{Nystrr om methods. We studied compositions using several extra stages, optimising the eeciency. An eeective error, E f , is deened and an extensive search is carried out using the extra parameters. The new methods have smaller values of E f than other methods found in the literature. When applied...
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A numerical method for solving Hamiltonian equations is said to be symplectic if it preserves the symplectic structure associated with the equations. Various symplectic methods are widely used in many fields of science and technology. A symplectic method preserves an approximate Hamiltonian perturbed from the original Hamiltonian. It theoretically supports the effectiveness of symplectic method...
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A number of conservative PDEs, like various wave equations, allow for a multi-symplectic formulation which can be viewed as a generalization of the symplectic structure of Hamiltonian ODEs. We show that Gauss-Legendre collocation in space and time leads to multi-symplectic integrators, i.e., to numerical methods that preserve a symplectic conservation law similar to the conservation of symplect...
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The non-linear wave equation is taken as a model problem for the investigation. Different multisymplectic reformulations of the equation are discussed. Multi-symplectic Runge–Kutta methods and multi-symplectic partitioned Runge–Kutta methods are explored based on these different reformulations. Some popular and efficient multi-symplectic schemes are collected and constructed. Stability analyses...
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Previously, it has been shown that discretising a multi-Hamiltonian PDE in space and time with partitioned Runge–Kutta methods gives rise to a system of equations that formally satisfy a discrete multisymplectic conservation law. However, these studies use the same partitioning of the variables into two partitions in both space and time. This gives rise to a large number of cases to be consider...
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ژورنال
عنوان ژورنال: Complexity
سال: 2019
ISSN: 1076-2787,1099-0526
DOI: 10.1155/2019/4025878