Topic
Ritz method
About: Ritz method is a research topic. Over the lifetime, 2090 publications have been published within this topic receiving 50016 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this paper, a method for accurate and efficient local density functional calculations (LDF) on molecules is described and presented with results using fast convergent threedimensional numerical integrations to calculate the matrix elements occurring in the Ritz variation method.
Abstract: A method for accurate and efficient local density functional calculations (LDF) on molecules is described and presented with results The method, Dmol for short, uses fast convergent three‐dimensional numerical integrations to calculate the matrix elements occurring in the Ritz variation method The flexibility of the integration technique opens the way to use the most efficient variational basis sets A practical choice of numerical basis sets is shown with a built‐in capability to reach the LDF dissociation limit exactly Dmol includes also an efficient, exact approach for calculating the electrostatic potential Results on small molecules illustrate present accuracy and error properties of the method Computational effort for this method grows to leading order with the cube of the molecule size Except for the solution of an algebraic eigenvalue problem the method can be refined to quadratic growth for large molecules
9,869 citations
14 Feb 2018
TL;DR: Deep Ritz Method as mentioned in this paper is a deep learning-based method for numerically solving variational problems, particularly the ones that arise from partial differential equations, and has the potential to work in rather high dimensions.
Abstract: We propose a deep learning-based method, the Deep Ritz Method, for numerically solving variational problems, particularly the ones that arise from partial differential equations. The Deep Ritz Method is naturally nonlinear, naturally adaptive and has the potential to work in rather high dimensions. The framework is quite simple and fits well with the stochastic gradient descent method used in deep learning. We illustrate the method on several problems including some eigenvalue problems.
1,586 citations
TL;DR: In this article, the free vibration of rectangular plates is analyzed using the Ritz method with 36 terms containing the products of beam functions, including clamped, simply-supported, and free edge conditions.
1,175 citations
TL;DR: In this article, the nonlinear free vibration of functionally graded nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) based on Timoshenko beam theory and von Karman geometric nonlinearity is investigated.
572 citations
TL;DR: In this article, a hyperbolic shear deformation theory applicable to bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates is presented.
527 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 34 |
| 2024 | 58 |
| 2023 | 61 |
| 2022 | 116 |
| 2021 | 105 |
| 2020 | 98 |