Numerical Methods Jobs (NOW HIRING)

NVIDIA pioneered accelerated computing. Today, we are building software, systems, and research platforms that help scientists and engineers solve problems that were once out of reach. We are looking for an Applied Research Scientist to join our computational engineering applied research team.

In this role, we will work together to design GPU-native numerical methods that make engineering simulation faster, more reliable, and easier to use across NVIDIA platforms, while providing the numerical foundations for emerging AI-native engineering algorithms. You will explore solver algorithms, build research prototypes, compare approaches on representative workloads, and help move promising ideas into software used by researchers, engineers, and partners. The goal is not simply to port established CPU algorithms, but to rethink methods around massive parallelism, hierarchical memory, reduced synchronization, mixed precision, tensor-core computation, and multi-GPU systems.

This role connects numerical analysis, accelerated computing, production-minded software engineering, and the co-design of future AI-native engineering methods. We are interested in candidates who enjoy working across math, code, hardware, and real engineering applications. Come help us shape the future of simulation on GPUs.

What you'll be doing: We work as a team, and you will help us: Invent and reformulate numerical algorithms whose mathematical and computational structure is co-designed for modern NVIDIA GPU architectures, including implicit and explicit engineering simulation. Develop linear and nonlinear solver approaches, including Newton-Krylov methods, multigrid and AMG, domain decomposition, matrix-free algorithms, mixed precision methods, sparse iterative and direct methods, and preconditioning strategies. Investigate when established CPU-oriented numerical methods should be reformulated or replaced for GPU architectures, including new approaches to synchronization-avoiding Krylov methods, GPU-native multigrid and domain decomposition, matrix-free implicit methods, mixed-precision algorithms, and sparse direct/iterative hybrids.

Evaluate algorithms on workloads in mechanics, contact, thermal-fluid systems, electromagnetics, semiconductor process and device simulation, EDA, multiphysics, and related CAE domains. Collaborate with CUDA-X, Warp, solver engineering, NVIDIA Research, universities, and industry partners to move useful research from prototype to NVIDIA software capabilities. Help shape the long-term applied research roadmap for GPU-native numerical methods and their evolution toward AI-native computational engineering.

What we need to see: PhD or equivalent experience in computational mechanics, applied mathematics, scientific computing, computer science, aerospace, mechanical, civil engineering, or a related technical field. 5+ years of relevant work/research experience. Research or engineering experience with PDE discretization, finite element, finite volume, discontinuous Galerkin methods, nonlinear solvers, sparse linear algebra, preconditioning, or high-performance computing.

Experience writing numerical software in C++ and Python, plus experience developing or optimizing CUDA or GPU code. Experience using profiling, benchmarking, numerical validation, or performance analysis to improve algorithms on GPU or multi-GPU systems. Ability to communicate technical tradeoffs clearly and collaborate across research, engineering, product, and partner teams.

Ways to stand out from the crowd: Experience with implicit structural dynamics, nonlinear mechanics, contact, CFD, electromagnetics, multiphysics, semiconductor simulation, EDA, CAE, or CAD-connected engineering workflows. Contributions to or practical experience with PETSc, Trilinos, MFEM, libCEED, OpenFOAM, NVIDIA Warp, CUDA-X, cuSPARSE, cuSOLVER, or related computational science frameworks. Experience with industrial simulation, EDA, semiconductor, CAE, or CAD ecosystems, including Ansys, Abaqus, LS-DYNA, Siemens Simcenter, Dassault SIMULIA, Altair, Cadence, Synopsys, COMSOL, MathWorks, or comparable internal solver and design platforms.

Experience with distributed solvers using MPI, NCCL, asynchronous methods, or performance analysis on GPU clusters. Publications, patents, open-source work, or deployed software in computational science venues or communities such as SC, SIAM CSE, SIAM SISC, CMAME, IJNME, JCP, AIAA, USNCCM, WCCM, or related areas. Your base salary will be determined based on your location, experience, and the pay of employees in similar positions.

The base salary range is 192,000 USD - 304,750 USD for Level 4, and 224,000 USD - 356,500 USD for Level 5. You will also be eligible for equity and benefits. Applications for this job will be accepted at least until August 17, 2026.

This posting is for an existing vacancy. NVIDIA uses AI tools in its recruiting processes. NVIDIA is committed to fostering an inclusive work environment and proud to be an equal opportunity employer.

As we highly value diversity in our current and future employees, we do not discriminate (including in our hiring and promotion practices) on the basis of race, religion, color, national origin, gender, gender expression, sexual orientation, age, marital status, veteran status, disability status or any other characteristic protected by law.