3 results about "Boundary integral equations" patented technology

The present application relates to the technical field of numerical calculation, in particular to a large-scale boundary element iteration initial value generation method based on boundary information neural network, comprising: constructing a basic data set of a small-scale example to train a pre-constructed deep neural network architecture; inputting known physical quantities of a to-be-solved domain into a physical information neural network based on boundary integral equation constraint obtained after training to predict small-scale unknown physical quantities; mapping the small-scale unknown physical quantities to actual calculation points corresponding to a large-scale fast boundary element method by using a boundary integral equation, and aligning degrees of freedom to generate a large-scale initial vector of degrees of freedom; and inputting the large-scale initial vector of degrees of freedom into a large-scale fast boundary element iteration solver to perform iteration as an initial value. Thus, the defects of the existing large-scale fast boundary element method in processing complex engineering problems, such as slow iteration convergence and large influence of initial value selection on calculation efficiency, are solved.

This invention discloses a time-domain numerical method for calculating the hydrodynamic performance of ships in the field of marine hydrodynamics. The method includes: establishing a three-dimensional numerical model of the hull and free surface; decomposing the total velocity potential based on time-domain potential flow theory; constructing boundary integral equations; introducing a time-increasing monotonically increasing function to smooth the initial transient response; simultaneously iteratively solving the free surface evolution and the ship's six-degree-of-freedom motion equations; and achieving self-consistent coupling between flow field pressure and ship motion using a closed feedback loop. This method also supports nonlinear free surface boundary conditions, suppresses numerical dissipation through high-order extrapolation, and dynamically calculates the restoring force matrix based on surface element integrals, significantly improving the calculation accuracy and stability of ship motion response in confined waters. It is suitable for engineering prediction of complex conditions such as near-shore navigation, shallow water resonance, and shoreline reflection.

This invention relates to the field of capacitance calculation technology and discloses a fast algorithm for extracting parasitic capacitance in large-scale integrated circuits. This method combines the method of moments (MoM), a fast multipole algorithm for layered dielectrics, and overlapping region decomposition preprocessing techniques to construct a complete parasitic capacitance extraction solution. By directly introducing the Green's function for the layered dielectric, the numerical solution strictly satisfies the electric field transport conditions at the dielectric interface, and the electrostatic problem in the layered dielectric is transformed into boundary integral equations defined on the interconnect surface. Subsequently, the MoM is used to discretize these boundary integral equations, resulting in a large-scale dense system of linear algebraic equations. To improve solution efficiency, an efficient preprocessing strategy based on overlapping region decomposition is further designed, and combined with the matrix-free minimum residual iteration method and the layered fast multipole algorithm, achieving efficient solution with low computational and storage overhead.