In his great work, The World as Will and Representation, Schopenhauer analysed phenomena (representation or appearances) in the first half and noumenon (reality or the will to life) in the second half. All phenomenal being, Schopenhauer maintained, no matter how apparently diverse and different, shares noumenal being in common, which is universal, eternal, undifferentiated and not subject to cause and effect. Phenomenal being, on the contrary, including our sense of self, is completely illusory (part of the veil of Maya) and subject to time, space and causality. Thus Schopenhauer can be said to have engaged in phenomenalysis, the analysis of appearances, in the first part of his magnum opus and noumenalysis, the analysis of the reality behind appearances, in the second.
The relevance to animal ethics is as follows. Schopenhauer believed that since we all share noumenal being in common, to harm others, including animals, is to harm ourselves. Furthermore, he maintained that the will to life subjects us to a life of suffering (which is similar to the central tenet of Buddhism) but compassion is one of the ways (the others being contemplation and the dispassionate contemplation of art) that allows us momentarily to free ourselves from the power of the will to life, to escape the limitations of our egos and to rend the veil of Maya. Compassion requires that we not harm not just people but animals too.