multigrid

简明释义

英[ˈmʌltɪɡrɪd]美[ˈmʌltɪɡrɪd]

adj. 多栅的，多重网格的

英英释义

单词用法

同义词

反义词

例句

1.Based on the multigrid of FL027, partial fine mesh was implemented.

在FL027多重网格基础上作了局部加密。

2.The effective method involves water drive hydrocarbon migration model, multigrid and LSQR iteration.

该法是以水动力为油气运移模型，采用LSQR迭代、多重网格的加速计算方法。

3.The finite volume method is adopted on each layer. The high efficiency of this multigrid algorithm has been verified by calculating flows around a multielement airfoil.

采用四重网格，在每一层网格上采用有限体积法进行计算。

4.By use of multigrid method, this paper proposes a preconditioned iteration method solving the boundary value problem of elliptic equations, the proof of convergence is given.

利用多重网格法的思想，构造出一种求解椭圆型方程边值问题的预处理迭代格式，并给出了收敛性证明。

5.In this paper, multigrid fictitious boundary method(MFBM)is applied to direct numerical simulation of vortex-induced motions of multi-cylinders in viscous flows.

本研究利用多重网格虚拟边界有限元法（MFBM）数值模拟多圆柱涡激运动问题。

6.The algebraic multigrid method can avoid those defects.

代数多重网格法可以避免这些缺陷。

7.A multigrid algorithm is described in this paper, which can be used to obtain the finite element solution of rock mechanics and engineering problems.

描述了适用于岩石力学与工程问题有限元解的多重网格算法。

8.The implementation of multigrid methods can significantly reduce the computational time for solving large-scale problems.

实施多重网格方法可以显著减少解决大规模问题的计算时间。

9.In numerical analysis, multigrid methods provide a powerful framework for solving partial differential equations.

在数值分析中，多重网格方法提供了一个强大的框架，用于求解偏微分方程。

10.Researchers are exploring new algorithms that enhance the efficiency of multigrid techniques in fluid dynamics simulations.

研究人员正在探索增强多重网格技术在流体动力学模拟中效率的新算法。

11.By utilizing multigrid techniques, we can tackle larger datasets without compromising accuracy.

通过利用多重网格技术，我们可以处理更大的数据集而不影响准确性。

12.The multigrid approach allows for faster convergence of iterative solvers in computational physics.

多重网格方法允许在计算物理中更快地收敛迭代求解器。

作文

In the field of numerical analysis and computational mathematics, one of the most significant advancements has been the development of methods to solve partial differential equations (PDEs). Among these methods, the multigrid technique stands out due to its efficiency and effectiveness in handling large-scale problems. The term multigrid refers to a hierarchical approach that utilizes multiple levels of discretization to accelerate the convergence of iterative solvers. This method is particularly useful in applications where traditional solvers struggle to achieve optimal performance, such as in fluid dynamics, structural analysis, and heat transfer simulations.The basic idea behind multigrid is to take advantage of the fact that errors in the solution can occur at different scales. By solving the problem on coarser grids, we can eliminate low-frequency errors more efficiently than we could on a fine grid alone. Once the solution is approximated on a coarser grid, it is then refined and transferred back to finer grids, where high-frequency errors can be corrected. This process is repeated iteratively, allowing the solver to converge much faster than traditional single-grid methods.One of the key advantages of the multigrid method is its ability to reduce computational time significantly. In many cases, problems that would take hours or even days to solve using conventional methods can be solved in a matter of minutes with multigrid. This speed is crucial for researchers and engineers who need timely results to make informed decisions in their work.Moreover, the multigrid method is highly versatile and can be applied to a wide range of problems across various fields. For example, in computational fluid dynamics, multigrid techniques are employed to solve the Navier-Stokes equations, which describe the motion of fluid substances. The ability to efficiently handle these complex equations is essential for simulating real-world phenomena, such as weather patterns, ocean currents, and airflow over aircraft.In the realm of structural engineering, multigrid methods facilitate the analysis of large structures subjected to various loads and constraints. By accurately predicting how materials will respond under stress, engineers can design safer and more efficient buildings, bridges, and other infrastructure. Similarly, in heat transfer applications, multigrid allows for precise modeling of temperature distributions, which is vital for optimizing energy consumption and improving thermal management systems.Despite its advantages, implementing multigrid methods requires a solid understanding of both the mathematical principles involved and the specific characteristics of the problems being addressed. Researchers and practitioners must carefully choose the appropriate grid levels and smoothing techniques to ensure optimal performance. Additionally, while multigrid can dramatically improve convergence rates, it may not be suitable for all types of problems, particularly those with highly irregular geometries or discontinuities.In conclusion, the multigrid method represents a powerful tool in the arsenal of numerical analysts and engineers. Its ability to efficiently solve complex PDEs makes it invaluable in various scientific and engineering applications. As computational power continues to grow and new challenges arise, the importance of techniques like multigrid will only increase, paving the way for further advancements in our understanding of the natural world.

在数值分析和计算数学的领域中，解决偏微分方程（PDE）的一个重要进展是开发各种方法。 在这些方法中，multigrid 技术因其在处理大规模问题时的高效性和有效性而脱颖而出。术语 multigrid 指的是一种分层方法，它利用多级离散化来加速迭代求解器的收敛。这种方法在传统求解器难以达到最佳性能的应用中尤其有用，例如流体动力学、结构分析和热传递模拟。multigrid 背后的基本思想是利用解决方案中的错误可以发生在不同尺度上的事实。通过在粗网格上解决问题，我们可以比单独在细网格上更有效地消除低频误差。一旦在粗网格上近似出解，就会将其细化并转移回更细的网格，在那里可以纠正高频误差。这个过程反复进行，使得求解器的收敛速度比传统单网格方法快得多。multigrid 方法的一个主要优势是能够显著减少计算时间。在许多情况下，使用常规方法需要数小时甚至数天才能解决的问题可以在几分钟内通过 multigrid 解决。这种速度对于需要及时结果来做出明智决策的研究人员和工程师至关重要。此外，multigrid 方法高度通用，可以应用于各种领域中的广泛问题。例如，在计算流体动力学中，multigrid 技术被用来解决描述流体物质运动的纳维-斯托克斯方程。有效处理这些复杂方程的能力对模拟现实世界现象至关重要，例如天气模式、海洋电流和飞机周围的气流。在结构工程领域，multigrid 方法促进了大型结构在各种载荷和约束下的分析。通过准确预测材料在应力下的反应，工程师可以设计出更安全、更高效的建筑、桥梁和其他基础设施。同样，在热传递应用中，multigrid 允许精确建模温度分布，这对优化能源消耗和改善热管理系统至关重要。尽管有其优点，但实现 multigrid 方法需要对所涉及的数学原理和所处理问题的特定特征有扎实的理解。研究人员和从业者必须仔细选择适当的网格级别和平滑技术，以确保最佳性能。此外，虽然 multigrid 可以显著提高收敛速度，但它可能不适用于所有类型的问题，特别是那些具有高度不规则几何形状或不连续性的问题。总之，multigrid 方法代表了数值分析师和工程师工具箱中的强大工具。其有效解决复杂 PDE 的能力使其在各种科学和工程应用中不可或缺。随着计算能力的不断增长和新挑战的出现，像 multigrid 这样的技术的重要性将只会增加，为我们对自然世界的进一步理解铺平道路。