An improved procedure for solving transient heat conduction problems using the boundary element method

In employing the boundary element method to solve transient heat conduction problems, domain integrals need to be calculated. These integrals can be calculated either by directly discretizing the domain, or indirectly by utilizing a time‐marching scheme which requires the time integrations to be evaluated from the initial time. Although the second approach overcomes the need for domain discretization, it has the disadvantage of requiring large storage and CPU time for increasing number of time steps. This paper is concerned with a procedure which approximates the domain integrals without the need for domain discretization. The time‐marching scheme is employed so that the domain integrals can be calculated at a particular time with a known weighting and temperature distribution. These integrals can then be utilized to approximate similar domain integrals with a different weighting. It is shown that the method proposed dramatically reduces the storage requirements and CPU time, even for a small number of time divisions.