An extraction technique for accurately computing steady state temperatures in high gradient regions -- theory (Q1891912)

The rationale of the extraction technique is presented in this paper, separately from its application in [ibid. 151-164 (1995, cf. the following review)]. In this technique, the high gradient portion of the temperature is mathematically extracted from the overall unknown temperature distribution. It is described in closed form (by an elementary function) and precisely obtained through energy considerations. The remaining portion of the temperature is rendered rapidly convergent, if Fourier series are used. Similarly, if numerical methods are employed, the extraction technique renders a rapidly convergent numerical process. We discuss extraction of the high gradient component along both a boundary and an interface. The former is intimately related to Gibbs phenomenon. Although the temperature problem is treated here, it should be noted that the same technique is applicable to any diffusion problem.