In this paper, we study the deep Ritz method for solving linear elasticity equation from a numerical analysis perspective. A modified formulation using $H^{1/2}(\Gamma_D)$ norm is introduced and analyzed in order to deal with (essential) Dirichlet boundary condition. We show that resulting provides best approximation among set of neural network (DNN) functions respect ``energy'' norm. Furthermo...

The objective of this paper is to present a comparative study of fitted-mesh finite difference method, Ritz-Galerkin finite element method and B-spline collocation method for a two-parameter singularly perturbed boundary value problems. Due to the small parameters ε and μ, the boundary layers arise. We have taken a piecewise-uniform fittedmesh to resolve the boundary layers and shown that fitte...

Trigonometric functions are among the most useful functions in the digital signal processing applications. The design introduced in this paper computes the trigonometric functions by means of the systolic arrays. The method for computing these functions for an arbitrary angle, , is the CORDIC algorithm. A simple standard cell is used for the systolic array. Due to the fixed inputs, in some...

Trigonometric functions are among the most useful functions in the digital signal processing applications. The design introduced in this paper computes the trigonometric functions by means of the systolic arrays. The method for computing these functions for an arbitrary angle, , is the CORDIC algorithm. A simple standard cell is used for the systolic array. Due to the fixed inputs, in some...

This paper describes an experimental study on the use of Ritz vectors for damage detection of a grid-type bridge model. A new procedure to extract Ritz vectors from experimental modal analysis is proposed and demonstrated using the test structure. Using appropriate load patterns, Ritz vectors can be made more sensitive to damage than modal vectors. The results indicate that the use of load-depe...

Abstract The parametric surrogate models for partial differential equations (PDEs) are a necessary component many applications in computational sciences, and the convolutional neural networks (CNNs) have proven to be an excellent tool generate these surrogates when fields present. CNNs commonly trained on labeled data based one-to-one sets of parameter-input PDE-output fields. Recently, residua...

Many composite cantilever plate-like structures have found engineering applications in different industries. For attaining a meaningful assessment of the plate vibration characteristics, it is important to efficient and effective methods for determining natural frequencies/mode shapes plates. In this paper, method formulated on basis Ritz simple first-order shear deformation theory (SFSDT) pres...