S U M M A R YWe present a new finite-element technique for calculating dynamic 3-D spontaneous rupture on an earthquake fault, which can reduce the required computational resources by a factor of six or more, without loss of accuracy. The grid-doubling technique employs small cells in a thin layer surrounding the fault. The remainder of the modelling volume is filled with larger cells, typically two or four times as large as the small cells. In the resulting non-conforming mesh, an interpolation method is used to join the thin layer of smaller cells to the volume of larger cells. Grid-doubling is effective because spontaneous rupture calculations typically require higher spatial resolution on and near the fault than elsewhere in the model volume. The technique can be applied to non-planar faults by morphing, or smoothly distorting, the entire mesh to produce the desired 3-D fault geometry. Using our FaultMod finite-element software, we have tested grid-doubling with both slip-weakening and rate-and-state friction laws, by running the SCEC/USGS 3-D dynamic rupture benchmark problems. We have also applied it to a model of the Hayward fault, Northern California, which uses realistic fault geometry and rock properties. FaultMod implements fault slip using common nodes, which represent motion common to both sides of the fault, and differential nodes, which represent motion of one side of the fault relative to the other side. We describe how to modify the traction-at-split-nodes method to work with common and differential nodes, using an implicit time stepping algorithm.The paper presents a new grid-doubling technique for dynamic 3-D spontaneous rupture calculations. This technique substantially reduces the required computational resources compared to standard finite-element techniques, without loss of accuracy.A dynamic 3-D spontaneous rupture calculation is a threedimensional numerical simulation of the physical processes that occur during an earthquake (see, e.g. Harris 2004). It is constructed by specifying the relevant physical laws, which include the elastodynamic wave equation, the constitutive equations which describe the rock properties, and the frictional equations which describe the properties of the fault. It is also necessary to specify a set of initial conditions, including the initial stresses acting on the fault. Then, the computer calculates the resulting behaviour of the system, which includes the nucleation and propagation of the earthquake rupture, and the resulting seismic waves.Such calculations are extremely computationally intensive. In finite-element approaches, space is discretized into a set of elements or cells. The standard technique is to use the same sized elements throughout all or most of the modelling volume. However, accurate modelling of fault frictional behaviour requires high spatial resolution, typically requiring an element size in the neighbourhood of 100 m or less. So, even relatively modest models may need many millions of elements. Models of that size consume so much computer...