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Herein, we present simulations of conductive filament formation in resistive random-access memory using a finite element solver. We consider the switching material, which is typically an oxide, as a two-phase material comprising low- and high-resistance phases. The low-resistance phase corresponds to a defective and conducting region with a high anion vacancy concentration, whereas the high-resistance phase corresponds to a non-defective and insulating region with a low anion-vacancy concentration. We adopt a phase variable correspondin