Selected Publications

B. K. Alpert and Yu Chen, A Representation of Acoustic Waves in Unbounded Domains, Communications in Pure and Applied Mathematics LVIII (10), 1358-1374 (2005).

D. F. Williams, B. K. Alpert, U. Arz, D. K. Walker, and H. Grabinski, Causal characteristic impedance of planar transmission lines, IEEE Transactions on Advanced Packaging 26 (2), 165-171, (2003).

B. Alpert, G. Beylkin, D. Gines, L. Vozovoi, Adaptive Solution of Partial Differential Equations in Multiwavelet Bases, Journal of Computational Physics 182, 149-190 (2002).

B. Alpert, L. Greengard, T. Hagstrom, Nonreflecting Boundary Conditions for the Time-Dependent Wave Equation, Journal of Computational Physics 180, 270-296 (2002).

Dylan F. Williams and Bradley K. Alpert, Causality and Waveguide Circuit Theory, IEEE Microwave Theory and Techniques. 49, 615-623 (2001).

B. Alpert, L. Greengard, T. Hagstrom, An Integral Evolution Formula for the Wave Equation, Journal of Computational Physics 162, 536-543 (2000). Erratum: Equation (10) should be G3(r,t)=1/(2 pi r).

Dylan F. Williams and Bradley K. Alpert, Characteristic Impedance, Power, and Causality, IEEE Microwave and Guided Wave Letters 9, 181-182 (1999).

Bradley Alpert, Leslie Greengard, and Thomas Hagstrom, Rapid Evaluation of Nonreflecting Boundary Kernels for Time-Domain Wave Propagation, SIAM Journal on Numerical Analysis 37, 1138-1164 (2000).

Bradley K. Alpert, Hybrid Gauss-Trapezoidal Quadrature Rules, SIAM Journal on Scientific Computing 20, 1551-1584 (1999).

Ronald C. Wittmann, Bradley K. Alpert, and Michael H. Francis, Nonideal Measurement Locations in Planar Near-Field Antenna Metrology, IEEE Antennas and Propagation Society International Symposium, July 14, 1997.

Ronald C. Wittmann, Bradley K. Alpert, and Michael H. Francis, Near-Field Antenna Measurements using Non-Ideal Measurement Locations, IEEE Transactions on Antennas and Propagation 46, 716-722 (1998). An earlier version appeared in proceedings, Antenna Measurement Techniques Association annual meeting, October, 1996.

Ruediger Jakob-Chien and Bradley K. Alpert, A Fast Spherical Filter with Uniform Resolution, Journal of Computational Physics 136, 580-584 (1997).

Bradley K. Alpert, "Accurate Discretization of Integral Operators," in NIST Special Publication 910, J. R. Berger and V. K. Tewary, editors, Green's Functions and Boundary Element Analysis for Modeling of Mechanical Behavior of Advanced Materials, December, 1996.

Bradley K. Alpert, High-Order Quadratures for Integral Operators with Singular Kernels, Journal of Computational and Applied Mathematics 60, 367-378 (1995).

Nathan A. Brilliant, Bradley K. Alpert, and Matt Young, "Video Microscopy Applied to Optical Fiber Geometry Measurements," NIST Technical Note 1369, November, 1994.

R. C. Wittmann and B. K. Alpert, "An Integral Occurring in Coherence Theory," SIAM Review 36, 655 (1994).

Bradley K. Alpert, A Class of Bases in L^2 for the Sparse Representation of Integral Operators, SIAM Journal on Mathematical Analysis 24, 246-262 (1993).

B. Alpert, G. Beylkin, R. Coifman, and V. Rokhlin, "Wavelet-Like Bases for the Fast Solution of Second-Kind Integral Equations," SIAM Journal on Scientific Computing 14, 159-184 (1993).

Bradley K. Alpert, Wavelets and Other Bases for Fast Numerical Linear Algebra, in Wavelets: A Tutorial in Theory and Applications, C. K. Chui, editor, Academic Press, New York, 1992.

Bradley K. Alpert, Construction of Simple Multiscale Bases for Fast Matrix Operations, in Wavelets and Their Applications, M. B. Ruskai, et al, editors, Jones and Bartlett, Boston, 1992.

Bradley K. Alpert and Vladimir Rokhlin, "A Fast Algorithm for the Evaluation of Legendre Expansions," SIAM Journal on Scientific and Statistical Computing 12, 158-179 (1991).