A method includes storing a first portion of a sparse triangular matrix in a local memory and launching a kernel for executing a set of workgroups. The first portion includes a plurality of row blocks, and each workgroup in the set of workgroups is associated with one of the plurality of row blocks. The method also includes, for each workgroup in the set of workgroups, solving the row block. The row block is solved by, for each row segment of a first subset of row segments in the row block, calculating a partial sum for the row segment based on one or more matrix elements in the row segment, and writing the partial sum to a remote memory of a first remote processing unit prior to terminating the kernel.