MADNESS (Multiresolution Adaptive Numerical Environment for Scientific Simulation) is a high-level software environment for the solution of integral and differential equations in many dimensions using adaptive and fast harmonic analysis methods with guaranteed precision based on multiresolution analysis [2] [3] and separated representations .

Finally, built upon the numerical tools are new applications with initial focus upon chemistry,[6] [7] , atomic and molecular physics,[8] material science, and nuclear structure.

The small matrix multiplication (relative to large, BLAS-optimized matrices) is the primary computational kernel in MADNESS; thus, an efficient implement on modern CPUs is an ongoing research effort.

[10] Adapting the irregular computation in MADNESS to heterogeneous platforms is nontrivial due to the size of the kernel, which is too small to be offloaded via compiler directives (e.g. OpenACC), but has been demonstrated for CPU–GPU systems .

The parallel runtime inside of MADNESS has been used to implement a wide variety of features, including graph optimization .