Generalized alternating‐direction collocation methods for parabolic equations. III. Nonrectangular domains

The alternating‐direction collocation (ADC) method is an efficient numerical approximation technique for the solution of parabolic partial differential equations. However, to date the ADC method has only been developed for rectangular discretizations. With judicious combination of isoparametric coordinate transformations and an extended ADC approach, the ADC method can be formulated on general nonrectangular domains. This extends the applicability of the ADC method by allowing it to be employed on domains of more general geometry.