boundary integral method

简明释义

边界积分法;

英英释义

例句

1.Using the boundary integral method 边界积分方法, we can efficiently model electromagnetic fields around conductive objects.

通过使用边界积分方法 boundary integral method，我们可以高效地模拟导电物体周围的电磁场。

2.The boundary integral method 边界积分方法 is particularly useful for problems with infinite or semi-infinite domains.

对于无限或半无限域的问题，边界积分方法 boundary integral method 特别有用。

3.Researchers applied the boundary integral method 边界积分方法 to analyze the stress distribution in a cracked material.

研究人员应用边界积分方法 boundary integral method 分析了裂纹材料中的应力分布。

4.In geophysics, the boundary integral method 边界积分方法 helps in solving potential flow problems.

在地球物理学中，边界积分方法 boundary integral method 有助于解决势流问题。

5.The boundary integral method 边界积分方法 is widely used in computational fluid dynamics to solve complex flow problems.

在计算流体动力学中，边界积分方法 boundary integral method 被广泛用于解决复杂的流动问题。

作文

The boundary integral method is a powerful mathematical technique used in various fields of engineering and applied mathematics. This method is particularly useful in solving problems related to partial differential equations (PDEs), which are common in the analysis of physical phenomena such as heat conduction, fluid flow, and electromagnetic fields. By transforming the PDEs into integral equations, the boundary integral method allows for the reduction of the dimensionality of the problem, making it easier to solve. One of the key advantages of the boundary integral method is its ability to handle infinite domains efficiently. In many physical applications, the region of interest extends to infinity, which poses significant challenges when using traditional numerical methods like finite difference or finite element methods. The boundary integral method circumvents this issue by only requiring the discretization of the boundary of the domain, rather than the entire volume. This leads to a significant reduction in computational effort and storage requirements. Moreover, the boundary integral method provides highly accurate solutions, especially for problems with singularities or sharp gradients. Since the method focuses on the boundaries, it captures the essential features of the solution without needing to resolve all the details within the domain. This property makes it particularly appealing for engineers and scientists who need precise results without excessive computational costs. In practical applications, the boundary integral method has been employed in various scenarios, including structural analysis, acoustic wave propagation, and fluid dynamics. For example, in structural engineering, the method can be used to analyze stress distribution in complex geometries subjected to external loads. Similarly, in fluid mechanics, it can model the behavior of fluid flow around obstacles, providing insights into drag forces and flow patterns. Despite its many advantages, the boundary integral method does have some limitations. One notable challenge is the treatment of nonlinear problems, which can complicate the formulation of the integral equations. Additionally, while the method excels in handling problems with well-defined boundaries, it may struggle with cases where the boundary conditions are not clearly specified. As technology continues to advance, the boundary integral method is being integrated with other numerical techniques, such as meshless methods and machine learning algorithms. This fusion of methodologies promises to enhance the capabilities of the boundary integral method, allowing it to tackle even more complex problems in science and engineering. Researchers are actively exploring new formulations and computational strategies to expand the applicability of the boundary integral method and improve its efficiency. In conclusion, the boundary integral method represents a significant advancement in the field of numerical analysis, offering a robust tool for solving a wide range of engineering problems. Its ability to simplify complex geometries and reduce computational demands makes it an attractive choice for researchers and practitioners alike. As we continue to explore the potential of this method, it is clear that the boundary integral method will play a crucial role in the future of computational mathematics and engineering design.

边界积分方法是一种强大的数学技术，广泛应用于工程和应用数学的多个领域。这种方法特别适用于解决与偏微分方程（PDE）相关的问题，这些方程在热传导、流体流动和电磁场等物理现象的分析中很常见。通过将PDE转化为积分方程，边界积分方法允许减少问题的维度，从而简化求解过程。边界积分方法的一个主要优点是其能够有效处理无限域。在许多物理应用中，感兴趣的区域延伸至无限，这在使用传统数值方法（如有限差分或有限元方法）时会产生重大挑战。边界积分方法通过仅要求对域的边界进行离散化，而不是整个体积，来规避这个问题。这大大减少了计算工作量和存储需求。此外，边界积分方法提供了高度准确的解决方案，特别是对于具有奇异性或急剧梯度的问题。由于该方法专注于边界，它能够捕捉到解的基本特征，而无需解析域内的所有细节。这一特性使得它在工程师和科学家需要精确结果而不产生过高计算成本时特别有吸引力。在实际应用中，边界积分方法已被用于各种场景，包括结构分析、声波传播和流体动力学。例如，在结构工程中，该方法可用于分析复杂几何形状在外部载荷下的应力分布。同样，在流体力学中，它可以模拟流体在障碍物周围的流动行为，提供有关阻力和流动模式的见解。尽管有许多优点，边界积分方法也有一些局限性。其中一个显著的挑战是非线性问题的处理，这可能会使积分方程的形式化变得复杂。此外，虽然该方法在处理具有明确边界的情况下表现出色，但在边界条件不明确的情况下可能会遇到困难。随着技术的不断进步，边界积分方法正在与其他数值技术（如无网格方法和机器学习算法）相结合。这种方法论的融合有望增强边界积分方法的能力，使其能够处理更复杂的科学和工程问题。研究人员正在积极探索新的公式和计算策略，以扩展边界积分方法的适用性并提高其效率。总之，边界积分方法代表了数值分析领域的一项重要进展，为解决广泛的工程问题提供了强有力的工具。其简化复杂几何形状和减少计算需求的能力，使其成为研究人员和从业者的理想选择。随着我们继续探索这一方法的潜力，显然边界积分方法将在计算数学和工程设计的未来中发挥关键作用。