Related papers: Adaptive algebraic multigrid on SIMD architectures
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
In lattice QCD computations a substantial amount of work is spent in solving linear systems arising in Wilson's discretization of the Dirac equations. We show first numerical results of the extension of the two-level DD-\alpha AMG method to…
Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…
Methods for solving hyperbolic systems typically depend on unknown ordering (e.g., Gauss-Seidel, or sweep/wavefront/marching methods) to achieve good convergence. For many discretisations, mesh types or decompositions these methods do not…
Algebraic multigrid (AMG) is often an effective solver for symmetric positive definite (SPD) linear systems resulting from the discretization of general elliptic PDEs, or the spatial discretization of parabolic PDEs. However, convergence…
Semiconductor spin qubits are a promising platform for large-scale quantum computing, but have yet to take full advantage of the broad class of quantum low-density parity check (QLDPC) codes, which promise high encoding rates and efficient…
Divergence constraints are present in the governing equations of numerous physical phenomena, and they usually lead to a Poisson equation whose solution represents a bottleneck in many simulation codes. Algebraic Multigrid (AMG) is arguably…
We present a novel differentiable grid-based representation for efficiently solving differential equations (DEs). Widely used architectures for neural solvers, such as sinusoidal neural networks, are coordinate-based MLPs that are both…
Algebraic multigrid (AMG) is one of the most efficient iterative methods for solving large sparse system of equations. However, how to build/check restriction and prolongation operators in practical of AMG methods for nonsymmetric {\em…
We present a parallel FFT algorithm for SIMD systems following the `Transpose Algorithm' approach. The method is based on the assignment of the data field onto a 1-dimensional ring of systolic cells. The systolic array can be universally…
The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated finite element…
In this paper, we develop an in-memory analog computing (IMAC) architecture realizing both synaptic behavior and activation functions within non-volatile memory arrays. Spin-orbit torque magnetoresistive random-access memory (SOT-MRAM)…
B-spline based orbital representations are widely used in Quantum Monte Carlo (QMC) simulations of solids, historically taking as much as 50% of the total run time. Random accesses to a large four-dimensional array make it challenging to…
Low bit-width Quantized Neural Networks (QNNs) enable deployment of complex machine learning models on constrained devices such as microcontrollers (MCUs) by reducing their memory footprint. Fine-grained asymmetric quantization (i.e.,…
Many problems in computational science and engineering involve partial differential equations and thus require the numerical solution of large, sparse (non)linear systems of equations. Multigrid is known to be one of the most efficient…
Processing-In-Memory (PIM) architectures offer a promising approach to accelerate Graph Neural Network (GNN) training and inference. However, various PIM devices such as ReRAM, FeFET, PCM, MRAM, and SRAM exist, with each device offering…
We propose a complex-valued neural-network (CV-NN) framework to optimally configure stacked intelligent surfaces (SIS) in next-generation multi-antenna systems. Unlike conventional solutions that separately tune analog metasurface phases or…
The standard goal for an effective algebraic multigrid (AMG) algorithm is to develop relaxation and coarse-grid correction schemes that attenuate complementary error modes. In the nonsymmetric setting, coarse-grid correction $\Pi$ will…
The stacked intelligent metasurface (SIM) emerges as an innovative technology with the ability to directly manipulate electromagnetic (EM) wave signals, drawing parallels to the operational principles of artificial neural networks (ANN).…
Many-Fermion Dynamics-nuclear, or MFDn, is a configuration interaction (CI) code for nuclear structure calculations. It is a platform-independent Fortran 90 code using a hybrid MPI+X programming model. For CPU platforms the application has…