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    • 3. 发明授权
    • Interpolation method, apparatus for carrying out the method, and control program for implementing the method
    • 插值方法,执行方法的装置以及用于实现该方法的控制程序
    • US07349936B2
    • 2008-03-25
    • US10632136
    • 2003-07-31
    • Akira AsaiShigeki Matsutani
    • Akira AsaiShigeki Matsutani
    • G06F7/38
    • G06F17/175
    • There is provided an interpolation method for the Volume-of-Fluid (VOF) applied to a two-phase incompressible fluid, in particular, which makes it possible to cause time evolution of a shape-describing function based on the Volume-of-Fluid (VOF) method while preserving a sharpness of a shape described by the function. The method defines a function F on a one-dimensional structured grid formed on a one-dimensional real region, the function being defined through definition of a value thereof at a center of each cell within the one-dimensional structured grid, as an interpolation function H. With respect to a cell of interest on the one-dimensional structured grid, a slope is set to zero if a forward difference and a backward difference of the function f have different signs, and to a value twice as large as a smaller one of absolute values of the forward difference and the backward difference if the forward difference and the backward difference have the same sign. The function F on a partial region of the one-dimensional real region determined by the cell of interest is defined by a linear function having a value of F0 at a center of the cell of interest and the slope.
    • 提供了一种应用于两相不可压缩流体的流体流体(VOF)的插值方法,特别地,这可以使基于流体体积的形状描述函数的时间演化 (VOF)方法,同时保持由该功能描述的形状的清晰度。 该方法定义了在一维实体区域上形成的一维结构网格上的函数F,该函数通过在一维结构化网格内的每个单元的中心定义其值作为内插函数来定义 对于一维结构化网格上的感兴趣的单元格,如果函数f的前向差和后向差具有不同的符号,则将斜率设置为零,并且将其设置为与小的两倍大的值 如果正向差和后向差具有相同的符号,则前向差和后向差的绝对值。 由感兴趣单元确定的一维实际区域的部分区域上的函数F由在关注单元格的中心处具有值F0的线性函数和斜率来定义。
    • 4. 发明授权
    • Optimization method with constraints and apparatus therefor
    • 具有限制和优化方法的优化方法
    • US07197486B2
    • 2007-03-27
    • US10192158
    • 2002-07-11
    • Akira AsaiShigeki Matsutani
    • Akira AsaiShigeki Matsutani
    • G06F7/10
    • G06Q10/04Y10S706/919
    • In a method for determining a minimum value of an optimization function under constraints given by equations, a set of points which satisfy the constraints is regarded as a Riemannian manifold within a finite-dimensional real-vector space, the Riemannian manifold is approached from an initial position within the real-vector space. An exponential map regarding a geodesic line equation with respect to a tangent vector on the Riemannian manifold ends at a finite order, an approximate geodesic line is generated as a one-dimensional orbit. An approximate parallel-translation is performed on the tangent vector on the Riemannian manifold and on the orbit generated in the orbit generating step by finite-order approximation of the exponential map regarding the parallel translation of the tangent vector. By repeating the above-described procedure from the position at which a minimum value is given until the minimum value on the orbit converges, the solution of the optimization problem with constraints is determined using a simple calculation procedure.
    • 在用等式确定的约束条件下确定优化函数的最小值的方法中,满足约束的一组点被认为是有限维实空间中的黎曼流形,黎曼流形从初始 在实数向量空间内的位置。 关于黎曼流形上的切线向量的测地线方程的指数图以有限的顺序结束,生成近似测线,作为一维轨道。 对黎曼流形上的切线向量和在轨道生成步骤中产生的轨道上的切线矢量进行近似平行平移,通过有限次逼近关于切线矢量的并行平移的指数图。 通过从给出最小值的位置重复上述过程直到轨道上的最小值收敛,使用简单的计算过程来确定具有约束的优化问题的解。