A finite difference wavefield modeling framework decouples the tasks of physical modeling and hardware-software optimization through the use of a platform-agnostic intermediate representation in the form of a dataflow graph. In at least some embodiments a wavefield simulation method includes specifying a kernel of operations to be applied at each point in a space and representing the kernel as a platform-agnostic dataflow graph. For each of multiple implementation platforms, the method further includes: deriving from the platform-agnostic graph a customized graph for the implementation platform; translating the customized graph into configuration information for the implementation platform; supplying the configuration information to the implementation platform to obtain a wavefield simulator; and employing the wavefield simulator to repeatedly apply said kernel of operations to each point in the space with specified input or output signals.