Shape sensitivity and optimization for transient heat diffusion problems using the bem

1995 ◽  
Vol 5 (4) ◽  
pp. 313-326 ◽  
Author(s):  
Doo Ho Lee ◽  
Byung Man Kwak
Keyword(s):  
Heat Diffusion ◽  
Shape Sensitivity ◽  
Transient Heat Diffusion ◽  
Diffusion Problems

scholarly journals Connections between peridynamics and graph Laplacian for diffusion problems

2020 ◽  
Author(s):  
Longzhen Wang ◽  
Florin Bobaru
Keyword(s):  
Boundary Conditions ◽  
Analytical Approach ◽  
Diffusion Processes ◽  
Time Integration ◽  
Graph Laplacian ◽  
Dirichlet Boundary Conditions ◽  
Heat Diffusion ◽  
Transient Heat Diffusion ◽  
Transfer Problems ◽  
Diffusion Problems

Formulations for diffusion processes based on graph Laplacian kernels have been recently used to solve linear transient heat transfer problems with insulated boundary conditions by way of a spectral-based semi-analytical approach. This has been called the “spectral graph” (SG) approach. In this paper we show that the meshfree discretizations for corresponding peridynamic models have a similar graph structure and lead to the same general equation as the SG approach. In this sense, the SG approach can be seen as a particular case of a peridynamic formulation. For the transient heat diffusion, we explain some differences between the SG approach and peridynamics, related to calibration and discretization procedures. We use a 1D heat diffusion example to highlight some limitations the spectral-based semi-analytical method in the SG approach has compared with the direct time-integration normally used in computing solutions to peridynamic models. We also introduce an extension of the semi-analytical approach to diffusion problems with Dirichlet boundary conditions.

A Time-Space Multi-Level Boundary Element Approach for Time-Dependent Heat Diffusion

2004 ◽  
Author(s):  
M. M. Grigoriev ◽  
G. F. Dargush
Keyword(s):  
Boundary Element ◽  
Space Time ◽  
Two Dimensions ◽  
Heat Diffusion ◽  
Time Dependent ◽  
Fast Time ◽  
Convolution Algorithm ◽  
Multi Level ◽  
Transient Heat Diffusion ◽  
Diffusion Problems

A new space-time multi-level boundary element method (MLBEM) is developed for transient heat diffusion problems in two-dimensions. This approach extends the MLBEM approach for steady heat diffusion [1] to accommodate fast time convolution algorithm [2]. The space-time MLBEM algorithm developed in this presentation provides fast, accurate and memory efficient numerical solutions for time-dependent heat diffusion problems. Conventional BEM approaches using M boundary elements result in operation counts of order O(M2N2) for the discrete time convolution over N time steps. Here we focus on the formulation for linear problems of transient heat diffusion and demonstrate reduced computational complexity to order O(M log MN3/2) for a two-dimensional model problem using the multi-level boundary element algorithm. Memory requirements are also significantly reduced, while maintaining the same level of accuracy as the conventional time domain BEM approach.

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