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We describe the design and application of new forward and inverse solvers developed for simulating synthetic resistance data and reconstructing the resistivity distribution of the subsurface in electrical resistivity tomography. The forward solver is based on the finite integration technique; the inverse solver is a domain search algorithm. These solvers were developed as necessary forward and inversion modelling tools to enable the optimisation of electrode positions in resistivity imaging to be explored. Numerical results from implementing these solvers show that they are successful for simulating and reconstructing the resistivity distribution in electrical resistivity tomography.