BAND project
https://bandframework.github.io
OpenBT Project
https://bitbucket.org/mpratola/openbt/src/master/
Software for Optimal Design
DPP-based Design Emulator is available as package demu on CRAN. Version 0.3.0 to be posted soon — adds sparse matrix support for sequential designs and fixes a few small bugs.
MPI BART
This is the original parallel code from the 2014 JCGS paper. It has not been maintained for some time, so YMMV.
Software for Computer Model Calibration
Bayesian Calibration for Stochastic Simulators (can also calibrate deterministic simulators) is available as package cmce on CRAN.
BART based calibration model: This file has some demo example R scripts. The actual code is C/C++ and is known to compile on Linux and OS X.