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The autoignition of dimethyl ether (DME) with temperature inhomogeneities is investigated by one-dimensional numerical simulations with detailed chemistry at high pressure and a constant volume. The primary purpose of the study is to provide an understanding of the autoignition of DME in a simplified configuration that is relevant to homogeneous charge compression ignition (HCCI) engines. The ignition structure and the negative temperature coefficient (NTC) behaviour are characterised in a homogeneous domain and one-dimensional domains with thermal stratification, at different initial mean temperatures and length scales. The thermal stratification is shown to strongly affect the spatial structure and temporal progress of ignition. The importance of diffusion and conduction on the ignition progress is assessed. It is shown that the effects of molecular diffusion decay relative to those of chemical reaction as the length-scale increases. This is to be expected, however the present study shows that these characteristics also depend on the mean temperature due to NTC behaviour. For the range of conditions studied here, which encompass a range of stratification length scales expected in HCCI engines, the effects of molecular transport are found to be small compared with chemical reaction effects for mean temperatures within the NTC regime. This is in contrast to previous work with fuels with single-stage ignition behaviour where practically realisable temperature gradients can lead to molecular transport effects becoming important. In addition, thermal stratification is demonstrated to result in significant reductions of the pressure-rise rate (PRR), even for the present fuel with two-stage ignition and NTC behaviour. The reduction of PRR is however strongly dependent on the mean initial temperature. The stratification length-scale is also shown to have an important influence on the pressure oscillations, with large-amplitude oscillations possible for larger length scales typical of integral scales in HCCI engines.