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Efficient shallow Ritz method for 1D diffusion problems
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DOI：10.1016/j.camwa.2025.10.020.png)
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Abstract
En 中文
This paper studies the shallow Ritz method for solving the one-dimensional diffusion problem. It is shown that the shallow Ritz method improves the order of approximation dramatically for non-smooth problems. To realize this optimal or nearly optimal order of the shallow Ritz approximation, we develop a damped block Newton (dBN) method that alternates between updates of the linear and non-linear parameters. Per each iteration, the linear and the non-linear parameters are updated by exact inversion and one step of a modified, damped Newton method applied to a reduced non-linear system, respectively. The computational cost of each dBN iteration is O(n).
Journal
C
IF:
2.5
Papers:
369
Citations:
1.8W