GPUs offer an order of magnitude higher compute power and memory bandwidth than CPUs. GPUs therefore might appear to be well suited to accelerate computations that operate on voluminous data sets in independent ways; e.g., for transformations, filtering, aggregation, partitioning or other "Big Data" style processing. Yet experience indicates that it is difficult, and often error-prone, to write GPGPU programs which efficiently process data that does not fit in GPU memory, partly because of the intricacies of GPU hardware architecture and programming models, and partly because of the limited bandwidth available between GPUs and CPUs.In this paper, we propose BigKernel, a scheme that provides pseudo-virtual memory to GPU applications and is implemented using a 4-stage pipeline with automated prefetching to (i) optimize CPU-GPU communication and (ii) optimize GPU memory accesses. BigKernel simplifies the programming model by allowing programmers to write kernels using arbitrarily large data structures that can be partitioned into segments where each segment is operated on independently; these kernels are transformed into BigKernel using straight-forward compiler transformations.Our evaluation on six data-intensive benchmarks shows that BigKernel achieves an average speedup of 1.7 over state-of-the-art double-buffering techniques and an average speedup of 3.0 over corresponding multi-threaded CPU implementations.